Question

assume that a procedure yield a binomial distribution with 2 trials and a probability of success of 0.90. use a binomial probability table to find the probability that the number of success is exactly 0. The probability that the number of success is exactly 0 is?

Answer 1

Let X be a binomial random variable with n = 2 and p = 0.90

X ~ Binomial ( n = 2, p = 0.90)

Probability mass function of X is,

P(X = x) = ⁿC_x p^x (1 - p)^n-x

We want to find, P(X = 0)

P(X = 0)

= ²C₀ * (0.90)⁰ * (1 - 0.90)^2-0

= 1 * 1 * (0.10)²

= 0.01

Therefore, the probability that the number of success is exactly 0 is 0.01