Question

In a large bag of marbles, 30% of them are red. a child chooses 4 marbles from this bag. if the child chooses the marbles at random, what is the chance that the child gets exactly three red marbles?

Answer 1

Probability of red is, P(R)=0.3
Probability of not red, P(R')=0.7

Possible outcomes with three reds are
R R R R' = 0.3×0.3×0.3×0.7 = 0.0189
R R R' R = 0.3×0.3×0.7×0.3 = 0.0189
R R' R R = 0.3×0.7×0.3×0.3 = 0.0189
R' R R R = 0.7×0.3×0.3×0.3 = 0.0189

Probability of getting exactly three marbles is = 4×0.0189 = 0.0756 = 7.56%