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Q.

In a locality, out of $5000$ people residing, $1200$ are above $30$ years of age and $3000$ are females. Out of the $1200$ who are above $30$ , two hundred are females. Suppose, after a person is chosen you are told that the person is a female. What is the probability that she is above $30$ years of age?

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a

\frac{1}{10}

b

\frac{1}{5}

c

\frac{1}{15}

d

None

answer is C.

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Detailed Solution

There are

5000 - 1200 = 3800

people under

30

if

1200

are above

30

.
The proportion of women under

30

is

3000 - 200 = 2800

Consequently, there are

200

over

30

and

2800

under

30

women.
The percentage of women over 30 is P(E) =

\frac{200}{3000} = \frac{1}{15}

Probability that she is above

30

years of age:

\frac{1}{15}

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In a locality, out of 5000 people residing, 1200 are above 30 years of age and 3000 are females. Out of the 1200 who are above 30, two hundred are females. Suppose, after a person is chosen you are told that the person is a female. What is the probability that she is above 30 years of age?