# Let S be the event that a cell phone

1. Let S be the event that a cell phone user switches carriers, and let D be the event that a cell phone user gets dropped a lot. Write the following probabilities and identify which are conditional and which are not conditional.

(a) The probability that a cell phone user switches carriers given that she gets dropped a lot.

p(S | D)

p(D | S)

p(S ∩ D)

Is the event conditional?

Yes No

(b) The probability that a cell phone user switches carriers and gets dropped a lot.

p(S | D)

p(D | S)

p(S ∩ D)

Is the event conditional?

Yes No

(c) The probability that a cell phone user gets dropped a lot given that she switches carriers.

p(S | D)

p(D | S)

p(S ∩ D)

Is the event conditional?

Yes No

If there are numbers needed here, I would need the table.

2. A single die is rolled. Find the probabilities of the given events. (Enter exact numbers as integers, fractions, or decimals.)

(a) rolling a 6

1 (b) rolling a 6, given that the number rolled is even 1/3 or 0.3333

2 (c) rolling a 6, given that the number rolled is odd 0.000

3

(d) rolling an even number, given that a 6 was rolled 1.00

4

3. In a newspaper poll concerning violence on television, 600 people were asked, "What is your opinion of the amount of violence on prime-time television−is there too much violence on television?" Their responses are indicated in the figure below.

Yes (Y)

No (N)

Don't Know (D)

Total

Men (M)

Women (W)

Total

use the data in the table above to find the given probabilities. (Round your answers to four decimal places.)

(A)

p(N)

What does p(N) represent?

*p(N) is the probability that a person surveyed said yes.

*p(N) is the probability that a man surveyed said no.

*p(N) is the probability that a person surveyed said no.

*p(N) is the probability that a man surveyed said yes.

(B)

p(W)

What does p(W)represent?

*p(W) is the probability that a person surveyed was a man.

*p(W) is the probability that a person surveyed was a woman.

*p(W) is the probability that a man surveyed said yes.

*p(W) is the probability that a woman surveyed said yes.

(C)

p(N | W)

What does p(N | W)represent?

p(N | W) is the probability that a woman surveyed said no.

p(N | W) is the probability that a woman surveyed said yes.

p(N | W) is the probability that a person surveyed who said yes was a woman.

p(N | W) is the probability that a person surveyed who said no was a woman.

(D)

p(W | N)

What does p(W | N)represent?

p(W | N) is the probability that a person surveyed who said no was a woman.

p(W | N) is the probability that a woman surveyed said yes.

p(W | N) is the probability that a woman surveyed said no.

p(W | N) is the probability that a person surveyed who said yes was a woman.

(E)

p(N ∩ W)

What does p(W ∩ N)represent?

p(W ∩ N) is the probability that a person surveyed said no given that the person was a woman.

p(W ∩ N) is the probability that a person surveyed was a woman and said no.

p(W ∩ N) is the probability that a person surveyed said yes and was a man.

p(W ∩ N) is the probability that a person was a woman given that the person said no.

(F)

p(W ∩ N)

What does p(W ∩ N) represent?

p(W ∩ N) is the probability that a person surveyed said no given that the person was a woman.

p(W ∩ N) is the probability that a person surveyed was a woman and said no.

p(W ∩ N) is the probability that a person surveyed said yes and was a man.

p(W ∩ N) is the probability that a person was a woman given that the person said no.

4. Cards are dealt from a full deck of 52. Find the probabilities of the given events. (Enter your answers as fractions.)

(a) The first card is a king.

(b) The second card is a king, given that the first was a king

(c) The first and second cards are both kings.

(d) Draw a tree diagram illustrating this.

5. A man and a woman have a child. Both parents are Tay-Sachs carriers. They know that their child does not have Tay-Sachs disease because she shows no symptoms, but they are concerned that she might be a carrier. Find the probability that she is a carrier. (Enter your answer as a fraction.)

6.

use the information in the table shown below to answer the exercise. (Round your answers to two decimal places.)

Type of Accident or Injury

Odds of Dying in 1 Year

Lifetime Odds of Dying

All transportation accidents

Pedestrian transportation accident

Bicyclist transportation accident

Motorcyclist transportation accident

Car transportation accident

Airplane and space transportation accident

All non-transportation accidents

Falling

Drowning

a) Find the probability that a U.S. resident dies from a motorcyclist transportation accident, given that the person dies from a transportation accident, in a lifetime.

b) Find the probability that a U.S. resident dies from a motorcyclist transportation accident, given that the person dies from a transportation accident, in one year.

c) Find the probability that a U.S. resident dies from a motorcyclist transportation accident, given that the person dies from an external cause, in one year.

7. Let P be the event that a student passes the course, and S be the event that a student studies hard. Write the following probabilities and identify which are conditional and which are not conditional

(A) The probability that a student passes the course given that the student studies hard.

p(S | P)

p(P | S)

p(P ∩ S)

Is this the conditional?

Yes or No?

(B) The probability that a student studies hard given that the student passes the course.

p(S | P)

p(P | S)

p(P ∩ S)

Is this the conditional?

Yes or No?

(C) The probability that a student passes the course and studies hard.

p(S | P)

p(P | S)

p(P ∩ S)

Is this the conditional?

Yes or No?

8. use the figure below. (Enter your answers as fractions.)

(a) Find p(B | A). 5/6

(b) Find p(B ∩ A). 2/3*5/6 = 10/18 = 5/9

9. Data on the governors of the fifty states are given in the table.

Democrats

Republicans

Independents

Male

14

26

0

Female

8

2

0

a) Find the probability that a governor is female, given that the governor is a Democrat. (Round your answer to four decimal places.)

B) Find the probability that a governor is female, given that the governor is a Republican. (Round your answer to four decimal places.)

10. In a newspaper poll concerning violence on television, 592 people were asked, "What is your opinion of the amount of violence on prime-time television — is there too much violence on television?"

use the data in the table above to find the following probabilities, where Y is the event "saying yes," and M is the event "being a man." (Round your answers to four decimal places.)

Which event, Y ' | M, Y | M', or Y ' | M', is the complement of the event Y | M?

Y | M'

Y ' | M

Y ' | M'

11. If a pair of dice is rolled times, use a tree diagram to find the probability that all throws result in. (Round your answer to four decimal places.)

12. A pair of dice is rolled. Find the probabilities of the given events. (Enter exact numbers as integers, fractions, or decimals.)

(a) The sum is.

(b) The sum is given that the sum is less than

(c) The sum is less than given that the sum is

(a) The probability that a cell phone user switches carriers given that she gets dropped a lot.

p(S | D)

p(D | S)

p(S ∩ D)

Is the event conditional?

Yes No

(b) The probability that a cell phone user switches carriers and gets dropped a lot.

p(S | D)

p(D | S)

p(S ∩ D)

Is the event conditional?

Yes No

(c) The probability that a cell phone user gets dropped a lot given that she switches carriers.

p(S | D)

p(D | S)

p(S ∩ D)

Is the event conditional?

Yes No

If there are numbers needed here, I would need the table.

2. A single die is rolled. Find the probabilities of the given events. (Enter exact numbers as integers, fractions, or decimals.)

(a) rolling a 6

1 (b) rolling a 6, given that the number rolled is even 1/3 or 0.3333

2 (c) rolling a 6, given that the number rolled is odd 0.000

3

(d) rolling an even number, given that a 6 was rolled 1.00

4

3. In a newspaper poll concerning violence on television, 600 people were asked, "What is your opinion of the amount of violence on prime-time television−is there too much violence on television?" Their responses are indicated in the figure below.

Yes (Y)

No (N)

Don't Know (D)

Total

Men (M)

Women (W)

Total

use the data in the table above to find the given probabilities. (Round your answers to four decimal places.)

(A)

p(N)

What does p(N) represent?

*p(N) is the probability that a person surveyed said yes.

*p(N) is the probability that a man surveyed said no.

*p(N) is the probability that a person surveyed said no.

*p(N) is the probability that a man surveyed said yes.

(B)

p(W)

What does p(W)represent?

*p(W) is the probability that a person surveyed was a man.

*p(W) is the probability that a person surveyed was a woman.

*p(W) is the probability that a man surveyed said yes.

*p(W) is the probability that a woman surveyed said yes.

(C)

p(N | W)

What does p(N | W)represent?

p(N | W) is the probability that a woman surveyed said no.

p(N | W) is the probability that a woman surveyed said yes.

p(N | W) is the probability that a person surveyed who said yes was a woman.

p(N | W) is the probability that a person surveyed who said no was a woman.

(D)

p(W | N)

What does p(W | N)represent?

p(W | N) is the probability that a person surveyed who said no was a woman.

p(W | N) is the probability that a woman surveyed said yes.

p(W | N) is the probability that a woman surveyed said no.

p(W | N) is the probability that a person surveyed who said yes was a woman.

(E)

p(N ∩ W)

What does p(W ∩ N)represent?

p(W ∩ N) is the probability that a person surveyed said no given that the person was a woman.

p(W ∩ N) is the probability that a person surveyed was a woman and said no.

p(W ∩ N) is the probability that a person surveyed said yes and was a man.

p(W ∩ N) is the probability that a person was a woman given that the person said no.

(F)

p(W ∩ N)

What does p(W ∩ N) represent?

p(W ∩ N) is the probability that a person surveyed said no given that the person was a woman.

p(W ∩ N) is the probability that a person surveyed was a woman and said no.

p(W ∩ N) is the probability that a person surveyed said yes and was a man.

p(W ∩ N) is the probability that a person was a woman given that the person said no.

4. Cards are dealt from a full deck of 52. Find the probabilities of the given events. (Enter your answers as fractions.)

(a) The first card is a king.

(b) The second card is a king, given that the first was a king

(c) The first and second cards are both kings.

(d) Draw a tree diagram illustrating this.

5. A man and a woman have a child. Both parents are Tay-Sachs carriers. They know that their child does not have Tay-Sachs disease because she shows no symptoms, but they are concerned that she might be a carrier. Find the probability that she is a carrier. (Enter your answer as a fraction.)

6.

use the information in the table shown below to answer the exercise. (Round your answers to two decimal places.)

Type of Accident or Injury

Odds of Dying in 1 Year

Lifetime Odds of Dying

All transportation accidents

Pedestrian transportation accident

Bicyclist transportation accident

Motorcyclist transportation accident

Car transportation accident

Airplane and space transportation accident

All non-transportation accidents

Falling

Drowning

a) Find the probability that a U.S. resident dies from a motorcyclist transportation accident, given that the person dies from a transportation accident, in a lifetime.

b) Find the probability that a U.S. resident dies from a motorcyclist transportation accident, given that the person dies from a transportation accident, in one year.

c) Find the probability that a U.S. resident dies from a motorcyclist transportation accident, given that the person dies from an external cause, in one year.

7. Let P be the event that a student passes the course, and S be the event that a student studies hard. Write the following probabilities and identify which are conditional and which are not conditional

(A) The probability that a student passes the course given that the student studies hard.

p(S | P)

p(P | S)

p(P ∩ S)

Is this the conditional?

Yes or No?

(B) The probability that a student studies hard given that the student passes the course.

p(S | P)

p(P | S)

p(P ∩ S)

Is this the conditional?

Yes or No?

(C) The probability that a student passes the course and studies hard.

p(S | P)

p(P | S)

p(P ∩ S)

Is this the conditional?

Yes or No?

8. use the figure below. (Enter your answers as fractions.)

(a) Find p(B | A). 5/6

(b) Find p(B ∩ A). 2/3*5/6 = 10/18 = 5/9

9. Data on the governors of the fifty states are given in the table.

Democrats

Republicans

Independents

Male

14

26

0

Female

8

2

0

a) Find the probability that a governor is female, given that the governor is a Democrat. (Round your answer to four decimal places.)

B) Find the probability that a governor is female, given that the governor is a Republican. (Round your answer to four decimal places.)

10. In a newspaper poll concerning violence on television, 592 people were asked, "What is your opinion of the amount of violence on prime-time television — is there too much violence on television?"

use the data in the table above to find the following probabilities, where Y is the event "saying yes," and M is the event "being a man." (Round your answers to four decimal places.)

Which event, Y ' | M, Y | M', or Y ' | M', is the complement of the event Y | M?

Y | M'

Y ' | M

Y ' | M'

11. If a pair of dice is rolled times, use a tree diagram to find the probability that all throws result in. (Round your answer to four decimal places.)

12. A pair of dice is rolled. Find the probabilities of the given events. (Enter exact numbers as integers, fractions, or decimals.)

(a) The sum is.

(b) The sum is given that the sum is less than

(c) The sum is less than given that the sum is

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