Question

The probability of winning a prize on a Scratch 'N Win ticket is 0.13. Assuming that the tickets are all independent of each other, what is the probability that it will take you at least 5 tickets before you win your first prize?

Round your answer to at least 3 decimal places.

Answer 1

Let X be the number of tickets you require before you win your first prize

To find P(X >= 5)

= P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + ..........

In all the cases only the last tick wins you the prize while the remaining tickets don't get the winning number

Thus, P( X = 5) =

P(X = 6) =

........

P(X = n) =

The sum is an infinite Geometric progression with

First term, a =

and common difference, r = 0.87

Thus, required probability =

= = 0.573