Question

Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places. P(X≥10), n=14, p=0.8

Answer 1

Given

n = 14 , p = 0.8

P( X 10) = P( X= 10 ) + P( X=11) + P(X= 12 ) + P( X= 13 ) +P(X= 14)

Using binomial probability

P(X =10) = n!/X!*(n-x)! *p^{​​​​​​X}​​​*(1-p)^n-x

P(X =10) = 14!/10!*4! * (0.8)¹⁰*(0.2)⁴ = 0.1720

P(X =11) = 14!/11!*3! *(0.8)¹¹*(0.2)³ = 0.2501

P(X = 12) = 14!/12!*2! *(0.8)¹²*(0.2)² = 0.2501

P( X = 13) = 14!/13!*1! *(0.8)¹³*(0.2)¹ = 0.1539

P(X = 14 ) = 14!/14!*0! *(0.8)¹⁴*(0.2)⁰ = 0.0440

P( X 10 ) = 0.1729+0.2501+0.2501+0.1539+0.0440

P(X 10) = 0.8702