If the probability of $$A$$ to fail in an examination is $$\frac{1}{5}$$ and that of $$B$$ is $$\frac{3}{{10}}$$ then the probability that either $$A$$ or $$B$$ fails is :
A.
$$\frac{1}{2}$$
B.
$$\frac{{11}}{{25}}$$
C.
$$\frac{{19}}{{50}}$$
D.
none of these
Answer :
$$\frac{{19}}{{50}}$$
Solution :
The probability of $$A$$ failing $$ = P\left( A \right) = \frac{1}{5}$$ and the probability of $$B$$ failing $$ = P\left( B \right) = \frac{3}{{10}}$$
The required probability
$$\eqalign{
& = P\left( {A\overline B \cup \overline A B} \right) = P\left( {A\overline B } \right) + P\left( {\overline A B} \right) \cr
& = P\left( A \right).P\left( {\overline B } \right) + P\left( {\overline A } \right).P\left( B \right) \cr
& = \frac{1}{5}\left( {1 - \frac{3}{{10}}} \right) + \left( {1 - \frac{1}{5}} \right).\frac{3}{{10}} \cr
& = \frac{{19}}{{50}}. \cr} $$
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.
$$\frac{{P\left( {\overline A } \right)}}{{P\left( {\overline B } \right)}}$$