Hope is the coach of the Wilson High School girls' soccer team. There are 3 minutes left in the game they are currently playing,

Question

2 years ago

7

Hope is the coach of the Wilson High School girls' soccer team. There are 3 minutes left in the game they are currently playing,

and they are losing by 1 goal. In the past, when losing by 1 goal, Hope has pulled a defender out of the game and replaced her with a forward a total of 9 times. When in the same position, she has left the defender in the game 10 times.
In the situations when Hope has pulled her defender, the team has lost 4 times, tied 2 times, and won 3 times. In situations when she has left her defender in the game, the team has lost 1 time, tied 3 times, and won 6 times.

Based on the information above, if the goal is to either tie or win the game, should Hope pull the defender or leave her in the game?

A.
Hope should not pull her defender.
B.
Hope should pull her defender.
C.
Hope pulling or not pulling her defender has no advantage.
D.
There is not enough information to determine if Hope should pull her defender or not.

Mathematics

2 answers:

NISA [10] · Answer 1 · 2022-01-04T12:42:57+03:00

To answer this question, we need to find the winning probability in either case.

Probability = no. of outcomes / total no. of possible outcomes

<u>When Hope pulled her defender :</u>

Total no. of games = 9

No. of games won = 3

Winning probability = 3/9 =1/3

<u>When Hope left her defender :</u>

Total no. of games = 10

No. of games won = 6

Winning probability = 6/10 = 3/5

We know that , 1/3 < 3/5.

So, Hope should not pull her defender, as the winning probability is better when Hope left her defender.

Answer : A. Hope should not pull her defender.

mamaluj [8] · Answer 2 · 2022-01-04T15:00:29+03:00

<h2>Answer:</h2>

Option: A is the correct answer.

Hope should not pull her defender.

<h2>Step-by-step explanation:</h2>

<u>When Hope has pulled her defender:</u>

The team has lost 4 times, tied 2 times, and won 3 times.

Hence, the total number of times she meets her goal is:

6 times

(Since the goal is to either tie or win the game )

Hence, the probability that she meets her goal is:

6/9=2/3=0.66

<u> When she has left her defender in the game:</u>

The team has lost 1 time, tied 3 times, and won 6 times.

Hence, the total number of times she meets her goal is:

9

Hence, the probability that she meets her goal is:

9/10=0.9

As the probability of meeting her goal is more when she left her defender in the game is more.

Hence, Hope should not pull her defender.