Question

The probability the Tim will sink a foul shot is 70%. If Tim attempts 25 foul shots, what is the probability that

a) he sinks exactly 21 shots

b) he sinks at least 21 shots

c) he sinks at most 21 shots

d) he sinks between 18 and 20 shots, inclusive.

Answer 1

Binomial distribution: P(X) = nCx p^x q^n-x

P(sinking a shot), p = 0.70

q = 1 - p = 0.30

n = 25

a) P(exactly 21) = 25C21 x 0.7²¹ x 0.3⁴

= 0.0572

b) P(at least 21) = P(21) + P(22) + P(23) + P(24) + P(25)

= 0.0572 + 25C22x0.7²²x0.3³ + 25C23x0.7²³x0.3² + 25x0.7²⁴x0.3 + 0.7²⁵

= 0.0572 + 0.0243 + 0.0074 + 0.0014 + 0.0001

= 0.0904

c) P(at most 21) = 1 - P(X > 21)

= 1 - (0.0243 + 0.0074 + 0.0014 + 0.0001)

= 0.9668

d) P(between 18 and 20, inclusive) = P(18) + P(19) + P(20)

= 25C18x0.7¹⁸x0.3⁷ + 25C19x0.7¹⁹x0.3⁶ + 25C20x0.7²⁰x0.3⁵

= 0.1712 + 0.1472 + 0.1030

= 0.4214