In a class $$30\% $$ students like tea, $$20\% $$ like coffee and $$10\% $$ like both tea and coffee. A student is selected at random then what is the probability that he does not like tea if it is known that he likes coffee ?
A.
$$\frac{1}{2}$$
B.
$$\frac{3}{4}$$
C.
$$\frac{1}{3}$$
D.
none of these
Answer :
$$\frac{1}{2}$$
Solution :
Let $$P\left( A \right) = $$ probability that a randomly selected student likes tea $$= 0.3.$$
Let $$P\left( {{A_2}} \right) = $$ probability that a randomly selected student does not like tea $$ = 1 - 0.3 = 0.7.$$
Let $$P\left( B \right) = $$ probability that a randomly selected student likes coffee $$= 0.2.$$
$$\eqalign{
& \therefore \,P\left( {{A_2} \cap B} \right) \cr
& = P\left( B \right) - P\left( {A \cap B} \right) \cr
& = 0.2 - 0.1 \cr
& = 0.1 \cr} $$
Now we have to find
$$P\left( {\frac{{{A_2}}}{B}} \right) = \frac{{P\left( {{A_2} \cap B} \right)}}{{P\left( B \right)}} = \frac{{0.1}}{{0.2}} = \frac{1}{2}$$
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.
$$\frac{{P\left( {\overline A } \right)}}{{P\left( {\overline B } \right)}}$$