Question

7/10 red candies, randomly pick 4, what is the probability that 2 or more of these 4 are red candies?

Answer 1

This is a direct application of Binomial distribution,

Let X be a number of red candies among 4 candies.

P(red candies) = 7/10 = 0.7

Here, X ~ Binomial ( n = 4, p = 0.7)

Probability mass function of X is,

P(X = x) = ⁿC_x p^x (1-p)^n-x

We want to find, P(X >= 2)

P(X >= 2)

= 1 - P(X <= 1)

= 1 - [ P(X = 0) + P(X = 1) ]

= 1 - [ 0.0081 + 0.0756 ]

= 1 - 0.0837

= 0.9163

P( X >= 2) = 0.9163

Hence, the probability that 2 or more of these 4 are red candies is 0.9163