Question

Free throws A basketball player has probability $0.75$of making a free throw. Explain how you would use each chance device to simulate one free throw by the player.

(a) A six-sided die

(b) Table D of random digits

(c) A standard deck of playing cards

Short answer

Part (a) If you roll a $1$or a $2,3$, the free throw is made by the basketball player.

Part (b) If the number is between $00$ and $74$, the basketball player makes the free throw (inclusive).

Part (c) The free throw will be made if the basketball player draws a diamond, hearth, or spade from the deck of cards.

Step-by-step solution

Part (a) Step 1. Given Information 

A basketball player's chance of making a free throw is$0.75$

Part (a) Step 2. Concept Used  

We can't foresee the outcomes of a chance process, yet they have a regular distribution over a large number of repetitions. According to the law of large numbers, the fraction of times a specific event occurs in numerous repetitions approaches a single number. The likelihood of a chance outcome is its long-run relative frequency. A probability is a number between $0$(never happens) and $1$(happens frequently) (always occurs).

Part (a) Step 3. Explanation  

We must first roll the six-sided die to simulate one free throw by the player utilizing each chance gadget and a six-sided die. If you roll a $1,2,3$the basketball player made the free throw. If you roll a $4$the basketball player misses the free throw. You must reroll the die if you receive a 5 or 6. As a result, we know that if you roll a $1,2$, or $3$, the basketball player made the free shot.

Part (b) Step 1. Explanation  

We've used Table D of random digits to replicate one free throw by the player using each chance device. Choose a line of random digits from Table D. Choose the first two digits of the number. The basketball player makes the free throw if the number is between $00$and $74$(inclusive). The basketball player misses the free throw if the number is between $75$and $99$(inclusive). As a result, we know that the basketball player makes the free throw if the number is between $00$and $74$(inclusive).

Part (c) Step 1. Explanation  

We have used each chance device to mimic one player free throw using a conventional deck of playing cards. Making a free throw has a probability of $0.75$or $3$out of $4$The following simulation is conceivable since diamonds, spades, clubs, and hearts are all equally likely: The basketball player makes the free throw if you pull a diamond, hearth, or spade from the deck of cards. The basketball player will miss the free throw if you draw a club from the deck of cards. As a result, we know that if the basketball player draws a diamond, hearth, or spade from the deck of cards, the free throw will be made.