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. A football player completes a pass 65.365.3% of the time. Find the probability that (a) the first pass he completes is the second pass, (b) the first pass he completes is the first or second pass, and (c) he does not complete his first two passes. 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. A football player completes a pass 65.365.3% of the time. Find the probability that (a) the first pass he completes is the second pass, (b) the first pass he completes is the first or second pass, and (c) he does not complete his first two passes. 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. A football player completes a pass 65.365.3% of the time. Find the probability that (a) the first pass he completes is the second pass, (b) the first pass he completes is the first or second pass, and (c) he does not complete his first two passes.

Explanation / Answer

Solution-

Let X be the random variable denoting the number at which first pass is made completely.

Then X follows negative binomial distribution with parameters k =1 and p = 0.65365

(a) P(X=2)

= 1c1 * (1-0.65365) * 0.65365

= 0.2264

(b) P(X=1 or X=2)

= P(X=1) + P(X=2)

= 0.65365 + 0.2264

= 0.88

(c) Let Y be the number of complete passes made then it follows binomial distribution with parameters n =2 and p = 0.65365

required probability = P(X=0)

= 2c0 * (0.65365)0 * (1-0.65365)2

= 0.1199

Answers

TY!

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