If the probability of Ronaldo will score at least 3 goals in

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BTGmoderatorLU: Moderator; Posts: 2505; Joined: Sun Oct 15, 2017 1:50 pm; Followed by:6 members

If the probability of Ronaldo will score at least 3 goals in

by BTGmoderatorLU » Wed Sep 26, 2018 2:19 pm

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Source: e-GMAT

If the probability of Ronaldo will score at least 3 goals in the match is 0.59 and the probability that Ronaldo's team will win the match is 0.73. What is the greatest probability that neither of the two events will occur?

A. 0.1107
B. 0.27
C. 0.41
D. 0.5693
E. 0.62

The OA is B.

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Source: Beat The GMAT — Problem Solving | Wed Sep 26, 2018 2:19 pm

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If the probability of Ronaldo will score at least 3 goals in

by Jay@ManhattanReview » Thu Sep 27, 2018 4:11 am

BTGmoderatorLU wrote:Source: e-GMAT

If the probability of Ronaldo will score at least 3 goals in the match is 0.59 and the probability that Ronaldo's team will win the match is 0.73. What is the greatest probability that neither of the two events will occur?

A. 0.1107
B. 0.27
C. 0.41
D. 0.5693
E. 0.62

The OA is B.

This is a tricky question.

It does not ask, "What is the probability that neither of the two events will occur?" It rather asks, "What is the greatest probability that neither of the two events will occur?"

Given:

1. Probability of Ronaldo's team winning the match = 0.73;

Thus, the probability of Ronaldo's team NOT winning the match = 1 - 0.73 = 0.27

2. Probability of Ronaldo scoring at least 3 goals = 0.59;

Thus, the probability of Ronaldo NOT scoring at least 3 goals = 1 - 0.59 = 0.41

Since we are asked to find out the greatest probability that neither of the two events will occur, let's assume that Ronaldo scores at least 3+ goals only when his team wins, thus, the greatest probability that neither of the two events will occur = 0.27.

This is a question on dependant probability. The answer 0.27*0.41 = 0.1107 were correct had the question asked, "What is the probability that neither of the two events will occur?"

The correct answer: B

Hope this helps!

-Jay
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Last edited by Jay@ManhattanReview on Thu Sep 27, 2018 9:49 pm, edited 1 time in total.

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ronaldo

by GMATGuruNY » Thu Sep 27, 2018 4:30 am

BTGmoderatorLU wrote:Source: e-GMAT

If the probability of Ronaldo will score at least 3 goals in the match is 0.59 and the probability that Ronaldo's team will win the match is 0.73. What is the greatest probability that neither of the two events will occur?

A. 0.1107
B. 0.27
C. 0.41
D. 0.5693
E. 0.62

Let G = at least 3 goals and NG = not at least 3 goals.
Let W = win the match and NW = not win the match.
Use a DOUBLE-MATRIX to organize the data:

The probability that Ronaldo will score at least 3 goals in the match is 0.59.
The probability that Ronaldo's team will win the match is 0.73.
Since G = 0.59, NG = 0.41.
Since W = 0.73, NW = 0.27.
The following matrix is yielded:

What is the greatest probability that neither of the two events will occur?
Since the rightmost box in the center row = 0.27, the greatest possible value for the center box -- which represents the probability that neither event occurs -- is 0.27:

s

The correct answer is B.

Last edited by GMATGuruNY on Thu Sep 27, 2018 5:29 am, edited 1 time in total.

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regor60: Master | Next Rank: 500 Posts; Posts: 416; Joined: Thu Oct 15, 2009 11:52 am; Thanked: 27 times

by regor60 » Thu Sep 27, 2018 5:24 am

BTGmoderatorLU wrote:Source: e-GMAT

If the probability of Ronaldo will score at least 3 goals in the match is 0.59 and the probability that Ronaldo's team will win the match is 0.73. What is the greatest probability that neither of the two events will occur?

A. 0.1107
B. 0.27
C. 0.41
D. 0.5693
E. 0.62

The OA is B.

The probability of losing the match is 1- 0.73 = 0.27.

Embedded in this are both scenarios of scoring goals, 3 or more, or less than 3.

To maximize the probability of both losing the match and scoring less than 3 goals, we have to minimize the probability of losing the match and scoring 3 or more goals, so we call that 0.

Since the probability of losing overall is 0.27 and the only scenario left is scoring less than 3 goals and losing, that scenario must have a probability of 0.27, B

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by Scott@TargetTestPrep » Tue Oct 02, 2018 6:20 pm

BTGmoderatorLU wrote:Source: e-GMAT

If the probability of Ronaldo will score at least 3 goals in the match is 0.59 and the probability that Ronaldo's team will win the match is 0.73. What is the greatest probability that neither of the two events will occur?

A. 0.1107
B. 0.27
C. 0.41
D. 0.5693
E. 0.62

Let A be the event that Ronaldo scores at least 3 goals in the match and let B be the event that Ronaldo's team wins the match. We have:

1 = P(A) + P(B) - P(A and B) + P(neither A nor B)

1 = 0.59 + 0.73 - P(A and B) + P(neither A nor B)

1 = 1.32 - P(A and B) + P(neither A nor B)

P(A and B) - 0.32 = P(neither A nor B)

Notice that we want the greatest value of P(neither A nor B), so we want the greatest value of P(A and B) also. The greatest value of P(A and B) is 0.59, and this occurs when A is a subset of B. Therefore, the greatest value of P(neither A nor B) is:

0.59 - 0.32 = P(neither A nor B)

0.27 = P(neither A nor B)

Answer: B

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