Question

In a jar of ten beads, seven are red and three are blue. a bead is drawn from the jar five times with replacement. what is the probability of seeing exactly 2 blue beads?

Answer 1

In a jar of ten beads; since 3 are blue; probability of picking a blue ball, B, = p(b) = 3/10. And P (of not picking a blue ball) ; p(b') = 7/10. Since it occurs with replacement, probabilities doesn't change Probaility of picking k blue balls from on n attempts is given by P_n(k) P_n(k) = (n, k) p^(k) q^(n -k) where p and q are b and b' respectively. P_5(2) = (5 , 2) (0.3)^(2) (0.7)^(5 - 2) P_5(2) = 5C2 (0.3)^(2) (0.7)^(3) = 0.3087