Family survey

A total of 160 families with 4 children each were surveyed with the following results.

Boys	4	3	2	1	0
Girls	0	1	2	3	4
Families	7	50	55	32	16

Let the probability of picking a boy or a girl be 1/2. Let P=boy, Q=girl.
What is the probability of getting:

a) All boys
b) three boys, one girl
c) two boys, two girls
d) one boy, three girls
e) All girls

Final Answer:

p₁ =  0.0438
p₂ =  0.3125
p₃ =  0.3438
p₄ =  0.2
p₅ =  0.1

Step-by-step explanation:

$$\begin{gathered} p_0=1/2=\frac{1}{2}=0.5 \\ n=160 \\ {p}_1=\frac{7}{n}=\frac{7}{160}=0.0438 \end{gathered}$$

$p_2=\frac{50}{n}=\frac{50}{160}=0.3125$

$p_3=\frac{55}{n}=\frac{55}{160}=0.3438$

$p_4=\frac{32}{n}=\frac{32}{160}=0.2$

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