Name _____________
Period ____
Honors Brief Calc
8.1 WS
Conditional Probability
Use the Venn diagram to find:
1. 𝑃(𝐸) =
2. 𝑃(𝐸 ∩ 𝐹) =
3. 𝑃(𝐸 ∪ 𝐹) =
4. 𝑃(𝐸/𝐹) =
5. 𝑃(𝐹/𝐸) =
6. 𝑃(𝐹̅) =
7. 𝑃(𝐸) = .2 𝑃(𝐹) = .4 𝑃(𝐸 ∩ 𝐹) = .1 Find the probability of E given F and the
probability of F given E.
8. If E and F are events with 𝑃(𝐹) =
5
4
13
and 𝑃(𝐸/𝐹) = 5, find 𝑃(𝐸 ∩ 𝐹)
Use the tree diagram for problems (9-12)
9. 𝑃(𝐶) =
10. 𝑃(𝐶/𝐵) =
11. P(D) =
12. P(D/B) =
9. 𝑃(𝐸) = .5 , 𝑃(𝐹) = .4, 𝑎𝑛𝑑 𝑃(𝐸 ∪ 𝐹) = .8 . Find P(F/E)
10a) For a 3-child family, find the probability of exactly 2 girls, given that the first child is a girl.
b) For a 3-child family, find the probability of exactly 1 girl, given that the first child is a boy.
11. From a box containing 3 white, 2 green, and 1 yellow ball, 2 balls are drawn one at a time
without replacing the first ball before the second is drawn. Find the probability that 1 white and 1
yellow ball are drawn.
12.
𝑃(𝐻) =
𝑃(𝐸 ∩ 𝐻) =
𝑃(𝐸/𝐻) =
Find the conditional probability for #13-14 and state in words the meaning of each one.
13.
a) 𝑷(𝑬/𝑮) =
b) 𝑷(𝑭/𝑮) =
14.
𝐚) 𝑷(𝑭/𝑰) =
𝐛) 𝑷(𝑴/𝑹 ∪ 𝑰) =
15. What is the probability that a randomly selected person has a blood type that is type B given
that the person is Rh-positive?
16. A marketing firm randomly sends a mass promotional mailing to 20% of the households in a
new market area. From experience the firm knows that the probability of response to a mailing is
.07. What is the probability that a household receives the mailing and responds?