Name _____________
Period ____
Honors Brief Calc
8.2 WS
Independent Events
1.If E and F are independent events, find P(F) if P ( E) = .2 and 𝑃(𝐸 ∪ 𝐹 ) = .3
2. If E and F are two independent events with P( E) = .2 and P(F) = .4, find
a) 𝑃(𝐸/𝐹) =
b) 𝑃(𝐹/𝐸) =
c) 𝑃(𝐸 ∩ 𝐹) =
d) 𝑃(𝐸 ∪ 𝐹) =
3. If P (E) = .3 and P(F) = .2. and 𝑃(𝐸 ∪ 𝐹) = .4, what is 𝑃(𝐸/𝐹) ? Are E and F independent?
4. A box has 10 marbles, 6 are red and 4 are white. Suppose we draw a marble from the box,
replace it, and then draw another. Find the probability that
a) both marbles are red
b) just one of the two marbles is red.
5. In a group of seeds, 1/3 of which should produce violets, the best germination that can be
obtained is 60%. If one seed is planted, what is the probability that it will grow into a violet?
Assume independence.
6. As a stockbroker, you recommend two stocks to a client. Each stock has a 60% probability of
increasing over the next year. Assuming that the performances of the two stocks are independent
of each other, what is the probability that both stocks will increase in value over the next year?
What is the probability that at least one stock will not increase in value?
7. A pumping station at a hydroelectric plant operates two identical pumps. Each pump has a
probability of failure of .05, and the probability that both pumps fail is .0025.
a) Are failures in the two pumps mutually exclusive? Explain.
b) What is the probability that at least one of the pumps fails?
c) Are failures in the two pumps independent?
8. A candidate for office believes that 2/3 of registered voters in her district will vote for her in
the next election. If two registered voters are independently selected at random, what is the
probability that
a) Both of them will vote for her in the next election?
b) Neither will vote for her in the next election?
c) Exactly one of them will vote for her in the next election?
9. A mouse runs through a T-maze 3 times. He can run to the right or to the left. Each outcome is
equally likely. List all the set of all possible outcomes. What is the probability that the mouse
will go left on the third run, given the mouse went left on the first run.