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Q.

State true or false.

1500 families with 2 children were randomly selected. The probability of a family chosen at random having 0, 1 and 2 daughters is $\frac{19}{60}$ , $\frac{407}{750}$ and $\frac{211}{1500}$ respectively.

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a

True

b

False

answer is B.

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Detailed Solution

It is given a statement 1500 families with 2 children were randomly selected. The probability of a family chosen at random having 0, 1 and 2 daughters is

\frac{19}{60}

,

\frac{407}{750}

and

\frac{211}{1500}

respectively.
Question Image

Probability of any event, P (E) = \frac{n (E)}{n (S)}

Number of favourable outcomes = n(E); Number of total outcomes = n(S); Probability of event = P(E)
It is given that 1500 families were randomly selected in total so the total number of outcomes, n(S)= 1500
When the favourable outcome is selecting a family with 0 daughters, n(E)=211
So, probability of event occurring will be,

\Rightarrow P (E) = \frac{n (E)}{n (S)}

\Rightarrow P (E) = \frac{211}{1500}

When the favourable outcome is selecting a family with 1 daughter, n(E)=814
So, probability of event occurring will be,

\Rightarrow P (E) = \frac{n (E)}{n (S)}

\Rightarrow P (E) = \frac{814}{1500}

\Rightarrow P (E) = \frac{407}{750}

When the favourable outcome is selecting a family with 2 daughters, n(E)=475
So, probability of event occurring will be,

\Rightarrow P (E) = \frac{n (E)}{n (S)}

\Rightarrow P (E) = \frac{475}{1500}

\Rightarrow P (E) = \frac{19}{60}

So, the probabilities of selecting a family with 0, 1 and 2 daughters are

\frac{211}{1500}

,

\frac{407}{750}

and

\frac{19}{60}

respectively.
Therefore, the given statement is false.
Hence option (2) is correct.

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