Question

Terry purchases 20 scratch off lottery tickets. Each ticket has a 9 % chance of winning. What is the probability that she has her first successful ticket on the 5 t h try? (Round to 4 decimal places) Geometric Probability

Answer 1

total tickets = 20

each ticket winning = 9% of 20

=1.8

probability of winning on each ticket = 1.8/20

= 0.09

probility of losing on each ticket = 1-0.09 = 0.91

here the trials are independent and geometric distribution is used,so

The geometric distribution gives the probability that the first occurrence of success requires kindependent trials, each with success probability p. If the probability of success on each trial is p, then the probability that the kth trial (out of k trials) is the first success is

${\displaystyle \Pr(X=k)=(1-p)^{k-1}p}$

for k = 1, 2, 3, ....

here, p = 0.09

1-p = 0.91

k= 5

so,

probability that she has her first successful ticket on the 5th trial = 0.91^5-1 * 0.09

= 0.91⁴ * 0.09

= 0.6857 *0.09

= 0.0617