CAMANISHPARMAR wrote:

A person is to be selected at random from the group T of people. What is the probability that the person selected is a member of club E?

1. The probability that a person selected at random from group T is not a member of club D and is not a member of club E is \(\frac{1}{4}\).

2. The probability that a person selected at random from group T is a member of club D and not a member of club E is \(\frac{5}{12}\).

Refer the affixed Venn diagram,

Question stem, probability that the person selected is a member of club E or a+c=?

statement-1:-

Given,he probability that a person selected at random from group T is not a member of club D and is not a member of club E is \(\frac{1}{4}\)

Or,\(n=\frac{1}{4}\)

we have, a+b+c+n=T

Or, (\(a+c)=T-n-b=1-\frac{1}{4}-b=\frac{3}{4}-b\)---------------(1) (T=1 because total probability is always 1)

Since 'b' is not provided, we can't determine a+c.

So, insufficient.

statement-2:-

Given, The probability that a person selected at random from group T is a member of club D and not a member of club E is \(\frac{5}{12}\)

Or, \(b=\frac{5}{12}\)--------------(2)

Since, we don't have info on "n", we can't determine a+c.

So, insufficient.

Now combining, from (1) & (2) we have \(a+c\)=\(\frac{3}{4}\)-\(\frac{5}{12}\)=\(\frac{1}{3}\)

Sufficient.

Ans. (C)

Hope it helps.

Attachments

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Regards,

PKN

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