Homework Problems for Conditional Probability
1. The probability that event A occurs is .63. The probability that event B occurs is .45. The probability that both events A and B occur is .18. Find the following:
A) P(A\B)
B) P(B\A)
2. The probability that event A occurs is .81. The probability that event B occurs is .68. The probability that both events A and B occur is .22. Find the following:
A) P(A\B)
B) P(B\A)
3. Two fair dice are rolled. Find the probability that the sum rolled is at least ten, given:
A) No information at all
B) At least one die comes up six
C) The same number appears on both dice
4. A card is drawn at random from a standard deck of playing cards. What is the probability that the card is less than a 7 given:
A) No information at all
B) The card is not a 2
C) The card is a heart
D) The card is a 3 or 4
5. If a fair coin is flipped three times, what is the probability that it comes up tails at least once given:
A) No information at all
B) All three flips produce the same side
C) It comes up tails at most once
D) The third flip is heads
E) It comes up heads at least once
6.
|
Religion/Ethnic background |
Italian |
Spanish |
Total |
|
Catholic |
145 |
122 |
267 |
|
Baptist |
111 |
225 |
336 |
|
Total |
256 |
347 |
603 |
7. In a small town the given chart below reflects the sex and educational backgrounds of the townsmen. Let M, W, P, B and H denote the events of being a Man, Woman, PHd degree, BA or MA degree and High School Diploma respectively.
|
PHD |
BA or MA |
High School Diploma |
TOTAL |
|
|
MEN |
72 |
52 |
83 |
207 |
|
WOMEN |
75 |
91 |
102 |
268 |
|
TOTAL |
147 |
143 |
185 |
475 |
Suppose that one of these townsmen is selected at random. What is the probability:
A) The townsmen is a woman?
B) The townsmen is a man?
C) The townsmen has a High School Diploma?
D) The townsmen is a man given that the townmen has a PHd?
E) The townsmen has MA degree given that the person is a male?
F) The townsmen is a woman given that the townmen has a BA?
8. A family has three children. Find the probability of having two boy, given that at most one of the children are girls.
9. A family has three children. Find the probability of having one boy, given that at least one of the children are boys.
Homework Solutions
1A) .4
1B) .29
2A) .32
2B) .27
3A) 1/3 or .33
3B) .45
3C) .17
4A) .38
4B) .33
4C) .38
4D) 1
5A) .88
5B) .5
5C) .75
5D) .75
5E) .86
6A) .56
6B) .57
6C) .67
6D) .54
7A) P(W)= .56
7B) P(M)= .44
7C) P(H) = .39
7D) P(M\P) = .49
7E) P(B\M) = .25
7F) P(W\B) = .64
8) .75
9) .43