Question

20 shots are fired independently at one target. Every single shot hits
the target with a probability of 0.8.
We are looking for the probability that

a) exactly 4 hits are scored,
b) at least one goal is scored,
c) a maximum of 6 hits are scored.
Which distribution is to be used? Give the expected value of the corresponding random variable. on!

Answer 1

Answer : 20 shots are fired independently at one target. Every single shot hits the target with a probability of 0.8.

Solution :

Here, we use the binomial distribution with probability of success.

P(X=k) = nCk * p^k * q^n-k

n = 20

p = 0.8

q = 1-0.8

q = 0.2

a) the probability that exactly 4 hits are scored:

P(X=4) = 20C4 * 0.8^4 * 0.2^(20-4)

= 4845 * 0.4096 * 0

= 0

b) the probability that at least one goal is scored:

= 1 - P(no hit) = 1- (1-p)^20

= 1 - 0.2^20

= 1 - 0

= 1

c) the probability that maximum of 6 hits are scored:

P(maximum 6 hits) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4)+ P(X=5) + P(X=6)

= 0 + 0 + 0 + 0 + 0 + 0 + 0

= 0

Expected value = np

= 20 * 0.8

= 16