#10 (Pg 155) A fair coin (i.e., heads and tails are equally likely) is tossed th

Question

#10 (Pg 155) A fair coin (i.e., heads and tails are equally likely) is tossed three times. Let X be the number of heads observed in three tosses of this fair coin.

a. Find the probability distribution of X.

b. Find the probability that two or fewer heads are observed in three tosses.

c. Find the probability that at least one head is observed in three tosses.

d. Find the expected value of X.

e. Find the standard deviation of X.

#C.1. (Pg 161) Suppose that you want to find the probability that event A or event B will occur. If these two events are not mutually exclusive, explain how you would proceed.

#C.2. (Pg 161) “If two events are mutually exclusive, they must not be independent events.” Is this statement true or false? Explain your choice.

Explanation / Answer

Suppose A fair coin is tossed 3 times There are 23 =8 Possible outcomes. a Probability distribution of X 7/8 b Probability that two or fewer heads 1/2 c Probability that at least one heads 1/7 d expected value of X 3/2 e Standard deviation of X (3^2)/2 Possible Outcome 1 HHH 2 HHT 3 HTH 4 THH 5 TTH 6 THT 7 HTT 8 TTT

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