1000 families with 2 children were selected randomly, and the following data was recorded:
$\begin{matrix} Number of girls in a family & 2 & 1 & 0 Number of families & 400 & 350 & 250 \end{matrix}$

Compute the probability of a family, chosen at random, having
(i) 2 girls.
(ii) 1 girl.
(iii) no girl.

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Solution

Total number of families = 400 + 350 + 250 = 1000

(i) Number of families having 2 girls = 400
$P_{1} (a randomly chosen family has 2 girls) = \frac{Number of families having 2 girls}{Total number of families}$
$P_{1} (a randomly chosen family has 2 girls) = \frac{400}{1000} = \frac{4}{10}$

(ii) Number of families having 1 girl = 350
$P_{2} (a randomly chosen family has 1 girl) = \frac{Number of families having 1 girl}{Total number of families}$
$P_{2} (a randomly chosen family has 1 girl) = \frac{350}{1000} = \frac{7}{20}$

(iii) Number of families having no girl = 250
$P_{3} (a randomly chosen family has no girl) = \frac{Number of families having no girl}{Total number of families}$
$P_{3} (a randomly chosen family has no girl) = \frac{250}{1000} = \frac{1}{4}$

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\begin{matrix} N u m b e r o f g i r l s i n a f a m i l y & 2 & 1 & 0 N u m b e r o f f a m i l i e s & 475 & 814 & 211 \end{matrix}

\begin{matrix} N u m b e r o f g i r l s i n a f a m i l y & 2 & 1 & 0 N u m b e r o f f a m i l i e s & 475 & 814 & 211 \end{matrix}

1500 families with 2 children were selected randomly, and the following data were recorded:

Number of girls in a family	2	1	0
Number of families	475	814	211

Compute the probability of a family, chosen at random, having

(i) 2 girls (ii) 1 girl (iii) No girl

Also check whether the sum of these probabilities is 1.

1500

2

No. of girls in a family	$2$	$1$	$0$
No. of families	$475$	$814$	$211$

2

1

1

\begin{matrix} N u m b e r o f b o y s i n a f a m i l y & 0 & 1 & 2 N u m b e r o f f a m i l i e s & 475 & 814 & 211 \end{matrix}

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