Question

Consider a sample of 10 randomly selected employees at an auditing firm. The probability that 3 employees in this sample have an honours degree is 0.215 while the probability that 4 employees in this sample have an honours degree is 0.251. Determine the probability that at least 2 employees in this sample have an honours degree.

Answer 1

Answer on Question #79537 — Math — Statistics and Probability

Question

Consider a sample of 10 randomly selected employees at an auditing firm. The probability that 3 employees in this sample have an honours degree is 0.215 while the probability that 4 employees in this sample have an honours degree is 0.251. Determine the probability that at least 2 employees in this sample have an honours degree.

Solution

P (3, 10) = 0.215

P (4, 10) = 0.251

P (>=2, 10) — ?

P (>=2, 10) = 1 - P (<= 1, 10) = 1 - C_{10}^{1} p^{1} (1 - p)^{9} - (1 - p)^{10}

P (3, 10) = C_{10}^{3} p^{3} (1 - p)^{7} = 120 p^{3} (1 - p)^{7} = 0.215

P (4, 10) = C_{10}^{4} p^{4} (1 - p)^{6} = 210 p^{4} (1 - p)^{6} = 0.251

p^{3} (1 - p)^{7} = 0.00179

p^{4} (1 - p)^{6} = 0.001195

(p^{3} (1 - p)^{6}) (1 - p) = 0.00179

(p^{3} (1 - p)^{6}) p = 0.001195

p^{3} (1 - p)^{6} = 0.001195 + 0.00179 = 0.002985

p = 0.001195 / 0.002985 = 0.4

P (>=2, 10) = 1 - 10 p (1 - p)^{9} - (1 - p)^{10} = 1 - 0.04 - 0.006 = 0.954

Answer: 0.954.

Answer provided by https://www.AssignmentExpert.com