Question

Mrs. A wishes to purchase a dress and she went to the mall. The probabilitiy that she will find the dream dress from a randomly selected mall is 0.12. She will keep looking for it until she finds it. Let X denote the number of stores she looked at. X follows a geometric distribution with p = 0.12. a) What is the probability that she will find her dream dress in the fourth store. b) What is the probability that it will take least six stores until she find the dress.

Answer 1

(a)

p = 0.12

o,

q = 1 -p = 0.88

So,

P(4th trial = success) = q³ X p = 0.88³ X 0.12 = 0.6815 X 0.12 = 0.0818

So,

Answer is:

0.0818

(b)

P(At least 6 trials for a success) = 1 - [P(1st trial = success) + P(2nd trial = success) + P(3rd trial = success) + P(4th trial = success) + P(5th trial = success)]

=1 - [p + qp + q² p + q³ p + q⁴ p ]

= 1 - [ 1 + q + q² + q³ + q⁴] p

= 1 - [ 1 +0.88 + 0.88² + 0.88³ + 0.88⁴] 0.12

= 1 - [ 1 + 0.88 + 0.7744 + 0.6815 + 0.5997] 0.12

= 1 - (3.9356 X 0.12)

= 1 - 0.4723

= 0.5277

So,

Answer is:

0.5277