Question

If birth to a male child and birth to a female child are equal probable, then what is the probability that atleast one of the three children born to a couple is male?

• A. $\frac{4}{5}$
• B. $\frac{7}{8}$
• C. $\frac{8}{7}$
• D. $\frac{1}{2}$

Answer 1

Answer: (B)

$\frac{7}{8}$

P=Probable of male child

$=\frac{1}{2}$

$q=1-\frac{1}{2}=\frac{1}{2}$

No. of children$=3$

By binomial theorem

$f\left(x\right)=C_x^n{p}^x{q}^{n-x}=C_r^3\left(\frac{1}{2}\right)x\left({\frac{1}{2}}^{3-x}\right)$

Probability of at least 1 male child

$=f\left(1\right)+f\left(2\right)+f\left(3\right)=C_1^3\left(\frac{1}{2}\right)(\frac{1}{2}{)}^2+C_2^3(\frac{1}{2}{)}^2\left(\frac{1}{2}\right)+C_3^3(\frac{1}{2}{)}^3=3\times \frac{1}{8}+3\times \frac{1}{8}+1\times \frac{1}{8}=\frac{3}{8}+\frac{3}{8}+\frac{1}{8}=\frac{7}{8}$