Question

A hamburger chain’s game card has ten squares, each of which has a covering that can be rubbed off to

reveal what is pictured beneath. Seven squares show different foods, two squares show the same food,

and one square has an ‘X-YOU LOSE’ on it.

The game is played by rubbing the covering off the squares until either you get the pair and win, or you

get the ‘X’ and lose.

What is the probability that you will win this game?

Answer 1

Hamburger chain's game:

10 Squares : 7 squares different foods, 2 squares same food , one square with X-You lose it.

To win the game you must find the two 'good' squares before the one 'bad' square, out of ten uncovered one at a time. Call the other 7 squares 'okay'.

Suppose it takes k turns to until you win, where k is some number between 2 and 9.Then to have won you must have selected k−2 'okay' squares and 1 'good' square out of all the ways to select k−1 squares out of all 9, and then have selected the second 'good' square out of the 11−k remaining squares.

P(W) =