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ZeroSquare
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Each of the 25 balls in a certain box is either red, blue or white and 05 Jul 2026, 02:28
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quick doubt - why didnt we take PE = 1/2?
Bunuel
Each of the 25 balls in a certain box is either red, blue or white and has a number from 1 to 10 painted on it. If one ball is to be selected at random from the box, what is the probability that the ball selected will either be white or have an even number painted on it?


Probability that the ball is white: \(P(W)\)
Probability that the ball has an even number: \(P(E)\)
Probability that the ball is white and has an even number: \(P(W\&E)\)

Probability that the ball selected is white or has an even number:

\(P(W \ or \ E)=P(W)+P(E)-P(W\&E)\)

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

This implies \(P(W\&E)=0\), meaning there is no white ball with an even number.

\(P(W \ or \ E)=P(W)+P(E)-0\)

Not sufficient.

(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 -->

This implies \(P(W)-P(E)=0.2\). Multiple values are possible for \(P(W)\) and \(P(E)\), such as 0.6 and 0.4 OR 0.4 and 0.2.

Cannot determine \(P(W \ or \ E)\).

Not sufficient.

(1)+(2) \(P(W\&E)=0\) and \(P(W)-P(E)=0.2\), so:

\(P(W \ or \ E)=P(W)+P(E)-P(W\&E)=(P(E)+0.2)+P(E)-0=2P(E)+0.2\)

Still, multiple answers are possible. For instance, if \(P(E)=0.4\) (10 even balls), then \(P(W \ or \ E)=1\). But if \(P(E)=0.2\) (5 even balls), then \(P(W \ or \ E)=0.6\).

Not sufficient.

Answer: E.

Hope it helps.
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Each of the 25 balls in a certain box is either red, blue or white and 05 Jul 2026, 05:33
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ZeroSquare
quick doubt - why didnt we take PE = 1/2?

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We cannot take P(E) = 1/2 here.

The ball has a number from 1 to 10, but the question does not say that the numbers are evenly distributed among the 25 balls.

For example, there could be many balls numbered 2, or very few balls with even numbers. So the probability of selecting an even-numbered ball is not necessarily 1/2.
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