Question

Probability of 2 or less successes out of 8 trials if the probability of success is 0.75.

Answer 1

Solution:

n = 8

p = 0.75

q = 1 – p = 0.25

We have to find P(X≤2)

P(X≤2) = P(X=0) + P(X=1) + P(X=2)

P(X=x) = nCx*p^x*q^(n – x)

P(X=0) = 8C0*0.75^0*0.25^8 = 0.000015

P(X=1) = 8C1*0.75^1*0.25^7 = 0.000366

P(X=2) = 8C2*0.75^2*0.25^6 = 0.003845

P(X≤2) = 0.000015 + 0.000366 + 0.003845

P(X≤2) = 0.004226

Required probability = 0.004226