Question

An official from the securities commission estimates that 75% of all investment bankers have profited from the use of insider information. If 15 investment bankers are selected at random from the commission’s registry, find the probability that:

1. at most 10 have profited from insider information.
2. at least 6 have profited from insider information.
3. all 15 have profited from insider information.

Answer 1

X ~ Binomial (n,p)

Where n = 15 , p = 0.75

P(X) = ⁿC_x p^x (1-p)^n-x

a)

P (X <= 10) = 0.3135 (From binomial cumulative probability table)

b)

P( X >= 6) = 1 - P( X <= 5)

= 1 - 0.00079

= 0.9992

c)

P( X = 15) = ¹⁵C₁₅ 0.75¹⁵ 0.25⁰

= 0.0134