Question

Jamie is practicing free throws before her next basketball game. The probability that she makes each shot is 0.6. If she takes 10 shots, what is the probability that she makes exactly 7 of them? Round your answer to three decimal places.

Answer 1

Answer:

The probability that she makes exactly 7 of them is 0.215 in three decimal places.

Explanation:

It is given that the probability that jamie makes each shot is 0.6.

The probability of success, p=0.6

While the probability of failure, q= 1-p = 1-0.6 = 0.4

Total number of shots(n) = 10.

According to the binomial distribution, the probability of x success in n trial is

P=nCx((p)^x)((q)^(n-x))

where, n is total trials, x is number of success, p is probability of success and q is probability of failure.

The probability that she makes exactly 7 of them is.

P= 10C7*((0.6)^7) *((0.4)^3)

P= 120*0.0279936*0.064

P= 0.21499

Round up to 3 d.p = 0.215

Therefore the probability that she makes exactly 7 of them to three decimal places is 0.215

Answer 2

The probability that she makes exactly 7 of them is 0.215.

Explanation:

It is given that the probability that she makes each shot is 0.6.

The probability of success, p=0.6

The probability of failure, q= 1-p = 1-0.6 = 0.4

Total number of shots = 10.

According to the binomial distribution, the probability of r success in n trial is

`P=^nC_rp^rq^(n-r)`

where, n is total trials, r is number of success, p is probability of success and q is probability of failure.

The probability that she makes exactly 7 of them is

`P=^(10)C_7(0.6)^7(0.4)^(10-7)`

`P=(10!)/(7!(10-7)!)(0.6)^7(0.4)^(3)`

`P=0.214990848`

`P\approx 0.215`

Therefore the probability that she makes exactly 7 of them is 0.215.