Microsoft Word - stats-exam-one-A.doc
Test I - Form A
1. Define with an example:
A) Random experiment.
B) Sample space.
C) Independent events.
D) Mutually exclusive events.
2. If A and B are independent events, then prove that A' and B' are independent events.
3. The probability that Ms Brown buys а blue hat is 0.43, that she buys a green hat is 0.42 and
that she buys both colour hats is 0.11. Find the probability that she buys either a green hat or a
lue hat.
4. The probability that a company A finishes a project in time is 0.49 and that of company B is
0.43. Assuming that they work independently, find the probability that project is done in time by
either of these companies.
5. A) Define conditional probability.
B) If P(A) = 0.52, P(B) = 0.63, and P(A  B) = 0.8. Compute
P(A | B) and P(A' | B')
6. Three coins are tossed. Find the probability that "we get two tails."
7. Two dice are tossed. Find the probability that
A) The sum is 7 and the first die shows а 3.
B) The sum is 7 or the first die shows а 3.
8. Out of an urn containing 10 blue ma
les and 9 red ma
les, 6 ma
les are chosen at random.
Find the probability that we draw at most two blue ma
les.
9. There are three urns, the first one contains 7 red and 4 blue ma
les, the second one contains 5
ed and 6 blue ma
les, and the the third one contains 6 red and 5 blue ma
les. An urn is chosen
at random and three ma
les are drawn from it. Find the probability that we get exactly 2 red
ma
les.
10. Out of a group 5 men and 5 women, а committee of 5 people is formed. In how many ways
can this committee be formed if the committee consists of
A) Exactly three women.
B) At least three women
C) At most three women