Question

Rachel likes to play the crane game at the supermarket. If she puts in a quarter, moves the crane, and randomly drops it, the following probabilities describe her chances of obtaining something. Assume throughout the game successive game outcomes are independent events and that she never obtains two candies in the same game.

Outcome	Dum Dum	Tootsie Roll	Sweet Tarts	Nothing
Probability	0.25	0.1	0.3	0.35

Suppose that Rachel receives six quarters from an indulgent grandparent. She resolves to play the game until she gets three Dum Dums in a row or until she exhausts the quarters (whichever comes first). What is the probability she gets three Dum Dums in a row before running out of money?

This is a statistics homework question.

Answer 1

P(selecting a dum dum) = p 0.25

P(selecting not a dum dum) = q =0.75

The probability she gets three Dum Dums in a row before running out of money i.e it means we need to get 3 dum dum out of 6 quarters in a row.

Total possible cases are: pppqqq, qpppqq, qqpppq, qqqppp

The probability she gets three Dum Dums in a row before running out of money = 4 * 0.25^3*0.75^3 = 0.0264