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?

Answer 1

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

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} * p^(r) * (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} * 0.50^(7) * (1-0.50)^(10-7)`

=
`120 * 0.50^(7) * 0.50^(3)`

=
`120 * 0.50^(10)`

= 0.117

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