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...

Write your solutions to the exam questions on blank or lined paper. Please write legibly. answers have to be hand written clearly and work have to be shown. Must scan paperwork and turn it into a PDF document .


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 blue 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 marbles and 9 red marbles, 6 marbles are chosen at random. Find the probability that we draw at most two blue marbles. 9. There are three urns, the first one contains 7 red and 4 blue marbles, the second one contains 5 red and 6 blue marbles, and the the third one contains 6 red and 5 blue marbles. An urn is chosen at random and three marbles are drawn from it. Find the probability that we get exactly 2 red marbles. 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