Find the indicated probabilities using the geometric distribution, the Poisson d

Question

Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine if the events are unusual. If convenient, use the appropriate probability table or technology to find the probabilities Afootball player completes a pass 67.8% o the me. Find the probability that (a) P(the first pass he completes is the second pass)- a the rst pass he completes is he second pass b the st pass he completes is the stor second pass, and C he does no o ete his ist two passes. (Round to three decimal places as needed.) (b) P(the first pass he completes is the first or second pass- (Round to three decimal places as needed.) (c) P(he does not complete his first two passes)- Round to three decimal places as needed.) Which of the events are unusual? Select all that apply A. The event in part (a), P(the first pass he completes is the second pass), is unusual. B. C. D. The event in part (b), P(the first pass he completes is the first or second pass, is unusual. The event in part (c), P(he does not complete his first two passes), is unusual None of the events are unusual.

Explanation / Answer

Ans:

Geometric distribution:

P(x=k)=(1-p)k-1*p

(x is the number of trials until first success occurs)

here,p=0.678

a)P(k=2)=(1-0.678)*0.678=0.218

b)P(k=1 or 2)=0.678+(1-0.678)*0.678=0.896

c)it means that it takes more than 2 trials to get first success)

P(k>=3)=1-(k<=2)=1-0.896=0.104

None of the events are unusual(as all probabilities are >0.05)

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