Math 237 Test #Z Nov. 9 1. A coin is loaded so that the probability that it show

Question

Math 237 Test #Z Nov. 9 1. A coin is loaded so that the probability that it shows heads when tossed is ¾. The coin is tossed twice. Let A be the event "the first toss is heads", let B be the event "the second toss is heads', and let C he the event "the tosses show the same face a) Are the events A and B independent? Why or why not? b) Are the events A and C independent? Why or why not? c) Compute PICIA) 2. An urn contains 2 red balls and 1 green ball. A ball is selected at random with replacement twice. Let X be the number of times the red ball is selected a) What are the possible values of X? b) Compute the probability mass function af X. c) Compute E[X], the expected value of X d) Compute thevariance of X: Var(X-EX]-E[X], 3. A chest has 3 drawers, each containing a coin. One coin is silver on both sides, one is gold on both sides, and the third is silver on one side and gold on the other side. A drawer is chosen at random and one face of the coln is shown to be silver. What is the probability the other side is

Explanation / Answer

1) a) Events A and B are independent as the probability of one of the event does not affect the other. For example, probability of getting a heads in the second toss is not affected by the outcome of the first toss(whether heads or tails)

b) Events A and C are not independent as the probability of event C will change based on the outcome of the first toss.

c) P(C | A), Given A has occured, find the probability of getting same facess on both the tosses. Since the first toss showed heads, the second toss has to give heads for event C to take place. Therefore
P(C |A) = 3/4 = 0.75 (same as getting heads in second toss as event A is given)

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