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5-38.

A BETTER CHANCE OF WINNING

Each of the problems below describes two different games you can play with a random number generator. In each case, you will win if the random number generator gives you the indicated kind of number. Find the theoretical probability that you win each game below. Decide and justify whether Game I or Game II in each part, (a) through (c), gives you a better chance of winning.

Game I

Game II

1. Picking a prime number from the integers between $1$ and $20$

• Picking a prime number from the integers between $21$ and $40$

1. Picking a multiple of $5$ from the integers between $1$ and $20$

• Picking a multiple of $5$ from the integers between $1$ and $40$

1. Picking a multiple of $7$ from the integers between $1$ and $40$

• Picking a multiple of $6$ from the integers between $1$ and $25$

Find the percent chance that each event will occur and compare the results.

1. Game 1

2. Equal chance

3. Game 2