Game Show In a TV game show, a contestant is given five cards with a different digit on each and is asked to arrange them to match the price of a brand-new-car. If she gets the price right, she wins the car. What is the probability that she wins, assuming that she knows the first digit but must guess the remaining four?

To find:

The probability of winning of the contestant.

Approach:

The probability of an event E is given by,

P(E)=n(E)n(S)

Calculation:

The contestant knows the first digits, so the contestant needs to guess the remaining four digits only.

The numbers of ways in which the contestant can guess the remaining four digits will give the sample space.

Out of the sample space, only one element will be favorable.

The numbers of ways in which the contestant can guess the remaining four digits is,

n=4×3×2×1=24

The probability of winning of the contestant is,