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Probability — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsProbability2 Marks
Question
A husband and wife appear in an interview for two vacancies for the same post. The probability of husband's selection is $\frac{1}{7}$ and that of wife's selection is $\frac{1}{5}$. What is the probability that,
Only one of them will be selected?
✓

Answer

Given, Probability of Husband's (H) selection $=\frac{1}{7}$
$\text{P(H)}=\frac{1}{7}$
Probability of Wife's (W) selection $=\frac{1}{5}$
$\text{P(W)}=\frac{1}{5}$
P(Only one of them will be selected)
$=\text{P}\Big[(\text{H}\cap\overline{\text{W}})\cup(\overline{\text{H}}\cap\text{W})\Big]$
$=\text{P}(\text{H}\cap\overline{\text{W}})+\text{P}(\overline{\text{H}}\cap\text{W})$
$=\text{P(H)}\text{ P}(\overline{\text{W}})+\text{P}(\overline{\text{H}})\text{ P(W)}$
$=\text{P(H)}[1-\text{P(W)}]+[1-\text{P(H)}]\text{ P(W)}$
$=\frac{1}{7}\Big[1-\frac{1}{5}\Big]+\Big[1-\frac{1}{7}\Big]\frac{1}{5}$
$=\frac{1}{7}\times\frac{4}{5}+\frac{6}{7}\times\frac{1}{5}$
$=\frac{10}{35}$
$=\frac{2}{7}$
Required probability $=\frac{2}{7}$

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