Miscellaneous Question 71
In each question, there are two different statements given as Quantity I and Quantity II. You have to consider the statements individually and mark your answer accordingly as per the given condition.
(1) Quantity I > Quantity II
(2) Quantity I $<$ Quantity II
(3) Quantity I $\geq$ Quantity II
(4) Quantity I $\leq$ Quantity II
(5) Quantity I = Quantity II or relationship cannot be determined
- Out of 14 applicants for a job, there are 6 women and 8 men. It is desired to select 2 persons for the job.
Quantity I : Probability of selecting no woman
Quantity II : Probability of selecting at least one woman
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Correct Answer: 71. (2)
Solution: 71. (2) Quantity I :
Only men will be selected.
Total possible outcomes
$=$ Selection of 2 persons out of 14 persons
$={ }^{14} \mathrm{C}_{2}=\frac{14 \times 13}{1 \times 2}=91$
Total favourable outcomes
$={ }^{8} \mathrm{C}_{2}=\frac{8 \times 7}{1 \times 2}=28$
$\therefore$ Required probability
$=\frac{28}{91}=\frac{4}{13}$
Quantity II :
Total possible outcomes $=91$
Ways of selections
$=1$ male and 1 female or 2 females
$={ }^{8} \mathrm{C} _{1} \times{ }^{6} \mathrm{C} _{1}+{ }^{6} \mathrm{C} _{2}$
$\therefore 48+\frac{6 \times 5}{1 \times 2}=48+15=63$
$\therefore$ Required probability
$=\frac{63}{91}=\frac{9}{13}$
Clearly, quantity I < quantity II
BETA
