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White Ball

by Juggernaut_86 » Mon Sep 05, 2011 5:15 pm
Each of the 25 balls in a box is either red, blue, or white and has a number from 1-10 painted on it. If one ball is to be selected at random from the box, then what's the probability that the ball selected will either be white or have an even number painted on it?

(1) The probability that the ball will both be white and have an even number painted on it is 0.

(2) The probability that the ball will be white minus the probability that the ball will have an even number painted on it is 0.2.


OA is E but I was getting C

Can anyone please explain?

Thanks!
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by edvhou812 » Mon Sep 05, 2011 5:59 pm
In order to answer a probability question that asks "What is the probability of A or B happening?" one needs to use the formula of Probability of (A+B)- Probability of (A*B). However neither statement gives us the information that is needed to solve the formula.

1) All we know is that there are not any white balls with an even number painted on it. (Insufficient)

2) a-b = 20% Does not tell us the value of A or B. (Insufficient)

1/2) All we have is that none of the white balls have even numbers, and that a-b=20%. We needed to be able to find the value of A and B to solve, but the two data points don't give us anything. (Insufficient)

Answer: E
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by Juggernaut_86 » Mon Sep 05, 2011 8:15 pm
Thanks for replying edvhou812.

Assuming A - Selection of a white ball. P(A) = unknown
and B - Selection of an even number. Would P(B) not be 0.5 since the probability of getting an even number from a set of numbers 1-10 is 0.5?

Probability of A or B happening if A and B are mutually exclusive events - P(A)+P(B)
Probability of A or B happening if A and B are not mutually exclusive events - P(A)+P(B)- P(A)P(B)- this equation should be used for this question.


Statement (1) states that P(A)P(B)= 0 - INSUFFICIENT
Statement (2) states that P(A)-P(B)= 0.2 - INSUFFICIENT

Statements (1) and (2) together
P(A)-P(B)=0.2 and since P(B)=0.5, P(A) will be 0.7
If we know P(A) and P(B) and we know that P(A)P(B)=0, can we not get the answer using 1 and 2?

Thanks
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by HeintzC2 » Fri Sep 16, 2011 11:22 am
The probability of getting an even is not necessarily 1/2. The question states that the balls have a number 1-10, but does not tell us the distribution of even to odd balls. Example:If every ball in the set has the #1 on it, that satisfies the criteria of the problem and P(even) = 0.

Juggernaut_86 wrote:Thanks for replying edvhou812.

Assuming A - Selection of a white ball. P(A) = unknown
and B - Selection of an even number. Would P(B) not be 0.5 since the probability of getting an even number from a set of numbers 1-10 is 0.5?
Probability of A or B happening if A and B are mutually exclusive events - P(A)+P(B)
Probability of A or B happening if A and B are not mutually exclusive events - P(A)+P(B)- P(A)P(B)- this equation should be used for this question.


Statement (1) states that P(A)P(B)= 0 - INSUFFICIENT
Statement (2) states that P(A)-P(B)= 0.2 - INSUFFICIENT

Statements (1) and (2) together
P(A)-P(B)=0.2 and since P(B)=0.5, P(A) will be 0.7
If we know P(A) and P(B) and we know that P(A)P(B)=0, can we not get the answer using 1 and 2?

Thanks
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