Chapter 5.1, Problem 13E

(a)

To determine

To explain how you would use each chance device to simulate one free throw by the player.

Explanation of Solution

To use each chance device to simulate one free throw by the player by a six sided die, we have,

First roll the six sided die.

If you roll a $1,2\text{ or 3}$ , then the basketball player made the free throw.

If you roll a $4$ , then the basketball player misses the free throw.

If you roll a $5\text{ or 6}$ , then roll the die again.

Thus, we know that, if you roll a $1,2\text{ or 3}$ , then the basketball player made the free throw.

(b)

To determine

To explain how you would use each chance device to simulate one free throw by the player.

Explanation of Solution

To use each chance device to simulate one free throw by the player by Table D of random digits, we have,

Pick a line of Table D of random digits.

Select the first two digit number.

If the number is between $00\text{ and 74}$ (including), then the basketball player makes the free throw.

If the number is between $\text{75 and 99}$ (including), then the basketball player misses the free throw.

Thus, we know that, if the number is between $00\text{ and 74}$ (including), then the basketball player makes the free throw.

(c)

To determine

To explain how you would use each chance device to simulate one free throw by the player.

Explanation of Solution

To use each chance device to simulate one free throw by the player by a standard deck of playing cards, we have,

The probability of making a free throw is $0.75\text{ or }3\text{ out of }4$ .

Since diamonds, spades, clubs and hearts are all equally likely, the following simulation is possible:

If you draw a diamond, hearth or spade from the deck of cards, then the basketball player makes the free throw.

If you draw a club from the deck of cards, then the basketball player fails to make the free throw.

Thus, we know that, if you draw a diamond, hearth or spade from the deck of cards, then the basketball player makes the free throw.