Exercise 3 Page 934

For the game of cards $43$ cards are used, including one joker. Four players are dealt $10$ cards each, and the remaining $3$ cards are put in a pile on the table. We know that Greg does not have the joker and want to find the probability that either his partner or the pile contains the joker. We can model this situation using a number line.

We will find the probability that either Greg's partner or the pile contains the joker by using geometric probability. Since Greg does not have the joker, we will randomly select a point on the segment that corresponds to the cards dealt to the other players and the pile.

The probability that the joker was dealt to Greg's partner or the pile is the ratio of the length of the segment corresponding to Greg's partner's and the pile's cards, to the length of the segment corresponding to the cards dealt to the pile and the players other than Greg.

As we can see, the length ${\ell }_1$ of the segment corresponding to the pile's and Greg's partner's cards is $13,$ while the length ${\ell }_2$ of the segment corresponding to the cards dealt to the pile and the players other than Greg is $33.$ Let's call the probability that either Greg's partner or the pile has the joker $P(A).$ Now, let's calculate $P(A).$ The probability that Greg's partner or the pile contains the joker is $\frac{13}{33},$ which can be written as a decimal as approximately $0.39,$ or as a percentage as approximately $39\%.$