Q81 / 160 · AP EAMCET 2019 (22 Apr Shift 1) · Mathematics

There are 800 families with four children in each family. Assuming equal chance for every child to be a boy or a girl, the number of families expected to have children of both sexes is

  • Correct answer
    A
    700
  • B
    100
  • C
    500
  • D
    300

Solution

Given that 4 children in each family. Event of expected to have children of both sexes \(=\frac{1}{2}\) \(\therefore\) Probability of children of both sexes \(\begin{aligned} & =1-[P(\text { all boys })+P \text { (all girls)}] \\ & =1-\left\{\left(\frac{1}{2}\right)^4+\left(\frac{1}{2}\right)^4\right\} \\ & =1-\left(\frac{1}{16}+\frac{1}{16}\right)=1-\frac{1}{8}=\frac{7}{8} \end{aligned}\) Hence, the probability for 800 families \(=\frac{7}{8} \times 800=700\)

Hence, the correct answer is option: 'A'.

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