IMG_0058 Que 4:The probability of success on any given attempt is p = 0.4The probability of failure on any given attempt is 1 - p = 1 - 0.4 = 0.6

a) P(exactly 4 attempts are required to get the first success)= P(failure on the first 3 attempts, then success on 4th attempt)= (0.6)^3 * (0.4)= 0.0864

b) The pmf of Number of attempts till first successX

P(X)1 2 3 4 5 6 7 8 90.6 0.24 0.096 0.0384 0.01536 0.006144 0.0024576 0.00098304 0.000393216

c) P(more than 1 attempt is required to get the first success)= P(failure on first attempt) = 0.6

d) P(exactly 10 attempts needed for 3rd success)= P(exactly 2 of the first 9 attempts are successful, then 10th attempt is

successful)= [(9 choose 2) p^2 * (1 - p)^(9-2)] * p

1

= (9 choose 2) p^3 * (1 - p)^7= 36 * (0.4)^3 * (0.6)^7= 0.0645

2