$1000$ families with $2$ children were selected randomly,and the following data were recorded:
Number of girls in a family $0$ $1$ $2$ Number of families $128$ $672$ $200$
Compute the probability of a family,chosen at random,having $(1)$ two girls,$(2)$ one girl.
| Number of girls in a family | $0$ | $1$ | $2$ |
| Number of families | $128$ | $672$ | $200$ |
Compute the probability of a family,chosen at random,having $(1)$ two girls,$(2)$ one girl.
(N/A) The total number of families is $1000$.
$(1)$ Let $E_1$ be the event that the chosen family has $2$ girls.
The number of families having $2$ girls is $200$.
Probability $P(E_1) = \frac{\text{Number of families with } 2 \text{ girls}}{\text{Total number of families}} = \frac{200}{1000} = 0.2$.
$(2)$ Let $E_2$ be the event that the chosen family has $1$ girl.
The number of families having $1$ girl is $672$.
Probability $P(E_2) = \frac{\text{Number of families with } 1 \text{ girl}}{\text{Total number of families}} = \frac{672}{1000} = 0.672$.
$(1)$ Let $E_1$ be the event that the chosen family has $2$ girls.
The number of families having $2$ girls is $200$.
Probability $P(E_1) = \frac{\text{Number of families with } 2 \text{ girls}}{\text{Total number of families}} = \frac{200}{1000} = 0.2$.
$(2)$ Let $E_2$ be the event that the chosen family has $1$ girl.
The number of families having $1$ girl is $672$.
Probability $P(E_2) = \frac{\text{Number of families with } 1 \text{ girl}}{\text{Total number of families}} = \frac{672}{1000} = 0.672$.
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