Answer:
68.47%
Step-by-step explanation:
The answer is 68.47%
Solution -
We know that,
The binomial formula is -
P(x) = [tex]^{n}C_{x}p^{x}q^{n-x}[/tex]
where
n is the number of trials
x is the strike out number.
p is the probability of success
q is the probability of failure
Here,
n = 8
p = 36% = 0.36
q = 1 - 0.36 = 0.64
Now,
We want to find the probability that he strikes out no more than 3 times (i.e. <= 3.)
So,
We need to check the cases where x = 0, 1, 2 and 3.
Now,
For x = 0,
P(0) = [tex]^{8}C_{0}(0.36)^{0}(0.64)^{8-0}[/tex] = (0.64)⁸
P(1) = [tex]^{8}C_{1}(0.36)^{1}(0.64)^{8-1}[/tex] = 8×0.35×0.64⁷ .
P(2) = [tex]^{8}C_{2}(0.36)^{2}(0.64)^{8-2}[/tex] = 28×0.35² ×0.64⁶ .
P(3) = [tex]^{8}C_{3}(0.36)^{3}(0.64)^{8-3}[/tex] = 56×0.35³ ×0.64⁵ .
So,
Probability that he strikes out no more than three times = P(0) + P(1) + P(2) + P(3) = 68.47%
