A man and a woman appear in an interview for two vacancies in the same post. The probability of man's selection is $$\frac{1}{4}$$ and that of the woman's selection is $$\frac{1}{3}$$. Then the probability that none of them will be selected is :
A.
$$\frac{1}{2}$$
B.
$$\frac{3}{4}$$
C.
$$\frac{2}{3}$$
D.
$$\frac{2}{5}$$
Answer :
$$\frac{1}{2}$$
Solution :
Let $$M$$ be the events that man will be selected and $$W$$ the events that woman will be selected. Then
$$\eqalign{
& P\left( M \right) = \frac{1}{4},\,\,{\text{so}}\,\,P\left( M \right) = 1 - \frac{1}{4} = \frac{3}{4} \cr
& P\left( W \right) = \frac{1}{3},\,\,{\text{so}}\,\,P\left( W \right) = \frac{2}{3} \cr} $$
Clearly $${M_1}$$ and $$W$$ are independent events. So,
$$\eqalign{
& P\left( {M \cap W} \right) = P\left( M \right) \times P\left( W \right) \cr
& = \frac{3}{4} \times \frac{2}{3} \cr
& = \frac{1}{2} \cr} $$
Releted MCQ Question on Statistics and Probability >> Probability
Releted Question 1
Two fair dice are tossed. Let $$x$$ be the event that the first die shows an even number and $$y$$ be the event that the second die shows an odd number. The two events $$x$$ and $$y$$ are:
Two events $$A$$ and $$B$$ have probabilities 0.25 and 0.50 respectively. The probability that both $$A$$ and $$B$$ occur simultaneously is 0.14. Then the probability that neither $$A$$ nor $$B$$ occurs is
The probability that an event $$A$$ happens in one trial of an experiment is 0.4. Three independent trials of the experiment are performed. The probability that the event $$A$$ happens at least once is
If $$A$$ and $$B$$ are two events such that $$P(A) > 0,$$ and $$P\left( B \right) \ne 1,$$ then $$P\left( {\frac{{\overline A }}{{\overline B }}} \right)$$ is equal to
(Here $$\overline A$$ and $$\overline B$$ are complements of $$A$$ and $$B$$ respectively).
A.
$$1 - P\left( {\frac{A}{B}} \right)$$
B.
$$1 - P\left( {\frac{{\overline A }}{B}} \right)$$
C.
$$\frac{{1 - P\left( {A \cup B} \right)}}{{P\left( {\overline B } \right)}}$$
D.
$$\frac{{P\left( {\overline A } \right)}}{{P\left( {\overline B } \right)}}$$