Question

A soccor player has a goal success rate of 42%. Each goal attempt made is independent of the others. Let ? represent the number of successfully made goals. Use the appropriate distribution to find the probability that the soccor player will make at most 4 goals in 9 attempts. (round to 4 decimal places)

Answer 1

solution

Given that ,

p = 0.42

1 - p = 1 - 0.42 = 0.58

n = 9

Using binomial probability formula ,

P(X = x) = (n C x) * px * (1 - p)n - x

P(X < 4 ) = P(X=0) +P(X=1)+P(X=2)+P(X=3)+P(X=4)

= (9 C 0) * 0.420 * (0.58)9 +(9 C 1) * 0.421 * (0.58)8 +(9 C 2) * 0.422 * (0.58)7 +(9 C 3) * 0.423 *(0.58)6 +(9 C 4) * 0.424 * (0.58)5

probability =0.6903