Question

Number of girls in the family 3,2,1,0 number of families 270,310,280,140 Find the probability of a family chosen at random has : 3 girl, 2 girl , 1 girl ,no girl Also check if the sum of probabilities is 1 or not​

Answer 1

Probability of a family chosen at random has 3 girls is 0.27

Probability of a family chosen at random has 2 girls is 0.31

Probability of a family chosen at random has 1 girl is 0.28

Probability of a family chosen at random has no girl is 0.14

Step-by-step explanation:

We are given the following information;

     Number of girls in the family                Number of families

                         3                                                      270

                         2                                                      310

                         1                                                       280

                         0                                                      140      

Probability of any event =  $\frac{\text{Favorable outcomes}}{\text{Total number of outcomes}}$

• Probability of a family having 3 girls = $\frac{\text{No. of families having 3 girls}}{\text{Total no. families}}$

Here, No. of families having 3 girls = 270

Total number of families = 270 + 310 + 280 + 140 = 1000

So, required probability = $\frac{270}{1000}$  =  0.27

• Probability of a family having 2 girls = $\frac{\text{No. of families having 2 girls}}{\text{Total no. families}}$

Here, No. of families having 2 girls = 310

Total number of families = 270 + 310 + 280 + 140 = 1000

So, required probability = $\frac{310}{1000}$  =  0.31

• Probability of a family having 1 girl = $\frac{\text{No. of families having 1 girl}}{\text{Total no. families}}$

Here, No. of families having 1 girls = 280

Total number of families = 270 + 310 + 280 + 140 = 1000

So, required probability = $\frac{280}{1000}$  =  0.28

• Probability of a family having 0 girl = $\frac{\text{No. of families having 0 girl}}{\text{Total no. families}}$

Here, No. of families having 0 girl = 140

Total number of families = 270 + 310 + 280 + 140 = 1000

So, required probability = $\frac{140}{1000}$  =  0.14

Now, Sum of all probabilities = 0.27 + 0.31 + 0.28 + 0.14 = 1

Therefore, Yes, the sum of probabilities is 1.