Let $X$ and $Y$ be two events of a sample space such that $P(X)=\frac{1}{3}$, $P(X|Y)=\frac{1}{2}$ and $P(Y|X)=\frac{2}{5}$, then which of the following is true?
- A$P(X \cap Y)=\frac{1}{5}$
- B$P(X \cup Y)=\frac{2}{5}$
- C$P(Y)=\frac{4}{15}$
- D$P(X \cup Y)=\frac{1}{2}$
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Let $A$ and $B$ be not mutually exclusive events. If $P(A) = \frac{4}{9}$ and $P(A \cap \bar{B}) = \frac{3}{7}$, then find $P\left(\frac{B}{A}\right)$.
Find $P(E | F)$ for a die thrown three times,where $E: 4$ appears on the third toss,and $F: 6$ and $5$ appear respectively on the first two tosses.
Easy
View Solution$E_1$ and $E_2$ are two independent events of a random experiment such that $P(E_1) = \frac{1}{2}$ and $P(E_1 \cup E_2) = \frac{2}{3}$. Match the items of List-$I$ with the items of List-$II$.
List-$I$ List-$II$ $A$. $P(E_2)$ $(i)$ $\frac{1}{2}$ $B$. $P(\frac{E_1}{E_2})$ $(ii)$ $\frac{5}{6}$ $C$. $P(\frac{\bar{E}_2}{E_1})$ $(iii)$ $\frac{1}{3}$ $D$. $P(\bar{E}_1 \cup \bar{E}_2)$ $(iv)$ $\frac{1}{6}$ $(v)$ $\frac{2}{3}$
| List-$I$ | List-$II$ |
| $A$. $P(E_2)$ | $(i)$ $\frac{1}{2}$ |
| $B$. $P(\frac{E_1}{E_2})$ | $(ii)$ $\frac{5}{6}$ |
| $C$. $P(\frac{\bar{E}_2}{E_1})$ | $(iii)$ $\frac{1}{3}$ |
| $D$. $P(\bar{E}_1 \cup \bar{E}_2)$ | $(iv)$ $\frac{1}{6}$ |
| $(v)$ $\frac{2}{3}$ |
In a hostel,$60 \%$ of the students read Hindi newspaper,$40 \%$ read English newspaper and $20 \%$ read both Hindi and English newspapers. $A$ student is selected at random. If she reads Hindi newspaper,find the probability that she reads English newspaper.
Easy
View SolutionIf the lengths of the sides of a triangle are decided by the three throws of a single fair die,then the probability that the triangle is of maximum area given that it is an isosceles triangle,is
DifficultJEE MAIN 2015
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