Jason is a very good bowler and has proven over the course of a season of league play that he gets a STRIKE 50% of t

Question

Jason is a very good bowler and has proven over the

course of a season of league play that he gets a

STRIKE 50% of the time. Using this empirical

probability what is the probability that Jason will get

exactly 7 strikes out of 10 attempts?

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Harper 3 months 2021-10-20T06:38:05+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-10-20T06:39:10+00:00

    Answer:

    The probability that Jason will get  exactly 7 strikes out of 10 attempts is 0.117.

    Step-by-step explanation:

    We are given that Jason is a very good bowler and has proven over the  course of a season of league play that he gets a  STRIKE 50% of the time.

    Also, Jason has been given 10 attempts.

    The above situation can be represented through binomial distribution;

    P(X = r) = \binom{n}{r} \times p^{r} \times (1-p)^{n-r};x=0,1,2,3,.......

    where, n = number trials (samples) taken = 10 attempts

                r = number of success = 7 strikes

                p = probability of success which in our question is % of the time

                       he gets a strike, i.e; p = 50%

    Let X = Number of strikes Jason get

    So, X ~ Binom(n = 10, p = 0.50)

    Now, probability that Jason will get  exactly 7 strikes out of 10 attempts is given by = P(X = 7)

                     P(X = 7)  =  \binom{10}{7} \times 0.50^{7} \times (1-0.50)^{10-7}

                                    =  120 \times 0.50^{7} \times 0.50^{3}

                                    =  120 \times 0.50^{10}

                                    =  0.117

    Therefore, the probability that Jason will get  exactly 7 strikes out of 10 attempts is 0.117.

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