Question

SO MANY POINTS

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.

Picking a prime number from the integers between 1 and 20

Picking a multiple of from the integers between 1 and 20

Picking a multiple of from the integers between 1 and 40​

Answer 1

Game 1

Equal chance

Game 2

Explanation:

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

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

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

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

Hint:

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

a.Picking a prime number from the integers between 21 and 40

b.Picking a multiple of 5 from the integers between 1 and 40

c.Picking a multiple of 6 from the integers between 1 and 25

Answer:

Game 1

Equal chance

game 2

Answer 2

a. In Game I, you have a theoretical probability of winning of 8/20 or 0.4. In Game II, you have a theoretical probability of winning of 6/20 or 0.3. Therefore, Game I gives you a better chance of winning.

b. In Game I, you have a theoretical probability of winning of 8/20 or 0.4. In Game II, you have a theoretical probability of winning of 0/20 or 0. Therefore, Game I gives you a better chance of winning.

c. In Game I, you have a theoretical probability of winning of 8/40 or 0.2. In Game II, you have a theoretical probability of winning of 0/40 or 0. Therefore, Game I gives you a better chance of winning.