Question

Two evenly matched tennis players, Jim and Rob, are going to play a set of 8 games. A player must win at least 6 of the 8 games to win the set. To find the probability of winning the set, Jim wants to simulate the situation using a number cube. If each roll represents a game, which associations on the cube correctly simulate the situation? Check all that apply.
Number 1 on the cube represents Jim, and number 3 represents Rob.

Even numbers on the cube represent Jim, and odd numbers represent Rob.

Numbers 1, 3, 4, and 5 represent Jim, and numbers 2 and 6 represent Rob.

Odd numbers on the cube represent Jim, and even numbers represent Rob.

Numbers 2 and 3 represent Jim, and numbers 1, 5, 4, and 6 represent Rob.

Answer 1

Answer:

The association that correctly simulate the situation is:

• Even numbers on the cube represent Jim, and odd numbers represent Rob.

• Odd numbers on the cube represent Jim, and even numbers represent Rob.

Step-by-step explanation:

We know that while doing some simulation our sample must be unbiased.

So, that the members have a equal opportunity of winning or losing a game i.e. there must be no biasing.

We know that a number cube has outcomes as:

{1, 2, 3, 4, 5, 6}

a)

Number 1 on the cube represents Jim, and number 3 represents Rob.

In this case if the remaining outcomes are:

{2,4,5,6}

in which none of the two wins.

So, such outcomes are just useless.

Hence, we can't have such a simulation.

b)

Number 1 on the cube represents Jim, and number 3 represents Rob.

In this case both the players have a equal chance of winning or losing the game.

i.e. 1/2

and also it covers all the possible outcomes.

Hence, such a simulation is good to perform a experiment.

c)

Numbers 1, 3, 4, and 5 represent Jim, and numbers 2 and 6 represent Rob.

In this the both the players don't have an equal chance of winning.

d)

Odd numbers on the cube represent Jim, and even numbers represent Rob.

In this case both the players have a equal chance of winning or losing the game.

i.e. 1/2

and also it covers all the possible outcomes.

Hence, such a simulation is good to perform a experiment.

e)

Numbers 2 and 3 represent Jim, and numbers 1, 5, 4, and 6 represent Rob.

Again both the players do not have a equal chance of winning.

Hence, it is not a correct way to simulate a situation.

Answer 2

The two correct answers are that even numbers represent Jim and odd numbers represent Rob, or odd numbers represent Jim and even numbers represent Rob.