Problem Solving

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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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