Suppose that a sharp-shooter hits the bull’s eye on a If the next 4 shots are target 18,000 in 50,000 shots. independent, find the probability that:
a. The next 4 shots hit the bull’s eye.
b. Two of the next 4 shots hit the bull’s eye
ANSWER:
Given that,
Suppose that a sharp-shooter hits the bull’s eye on a If the next 4 shots are target 18,000 in 50,000 shots. independent, find the probability that:
Binomial distribution used.
n=4, p=18000/50000 = 0.36
P(X=x) = (_{n}C_{x}) p^{x} (1-p)^{n-x}
The next 4 shots hit the bull’s eye.
P( x=4) =0.0168
Excel function used: =BINOM.DIST(4, 4, 0.36, FALSE)
Two of the next 4 shots hit the bull’s eye
P( x=2) =0.3185
Excel function used: =BINOM.DIST(2, 4, 0.36, FALSE)
Binomial probabilities Table | ||
X | P(X) | |
0 | 0.1678 | |
1 | 0.3775 | |
2 | 0.3185 | |
3 | 0.1194 | |
4 | 0.0168 |
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