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 67.4%

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.

(a) P(the first pass he completes is the second pass)=

Explanation / Answer

Let us denote ‘Success’ as the ‘Completion of Pass’. Given that probability of Success is 0.674.

Define the random variable

X : No. of passes made by a player before he makes first complete pass.

X : 0,1,2,…..

Here r.v. X ~ Geometric distribution with probability of success p=0.674

Therefore, pmf of X is

P[X=x] = p(1-p)x   x=0,1,2,…

P[X=1] = p(1-p) = 0.674 * 0.324 =

P[X 1] = P[X=0] + P[X=1] = 0.674 + 0.219724 =

P[X > 1] = 1 – P[X 1] = 1-0.893724 =

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.