$A$ random variable $X$ has the following probability distribution:
$X$ $0$ $1$ $2$ $3$ $4$ $P(X)$ $k$ $2k$ $4k$ $6k$ $8k$
The value of $P(1 < X < 4 \mid X \leq 2)$ is equal to:
| $X$ | $0$ | $1$ | $2$ | $3$ | $4$ |
| $P(X)$ | $k$ | $2k$ | $4k$ | $6k$ | $8k$ |
The value of $P(1 < X < 4 \mid X \leq 2)$ is equal to:
- A$\frac{4}{7}$
- B$\frac{2}{3}$
- C$\frac{3}{7}$
- D$\frac{4}{5}$
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Suppose $A$ and $B$ are events of a random experiment such that $P(A)=\frac{1}{3}$, $P(A \cap B)=\frac{1}{5}$ and $P(A \cup B)=\frac{3}{5}$. Match the items of List-$I$ with the items of List-$II$. List-$I$ List-$II$ $A$. $P(\frac{A}{B})$ $(i)$. $\frac{2}{15}$ $B$. $P(\bar{B})$ $(ii)$. $\frac{4}{15}$ $C$. $P(A \cap \bar{B})$ $(iii)$. $\frac{8}{15}$ $D$. $P(B \cap \bar{A})$ $(iv)$. $\frac{2}{3}$ $(v)$. $\frac{3}{7}$
| List-$I$ | List-$II$ |
| $A$. $P(\frac{A}{B})$ | $(i)$. $\frac{2}{15}$ |
| $B$. $P(\bar{B})$ | $(ii)$. $\frac{4}{15}$ |
| $C$. $P(A \cap \bar{B})$ | $(iii)$. $\frac{8}{15}$ |
| $D$. $P(B \cap \bar{A})$ | $(iv)$. $\frac{2}{3}$ |
| $(v)$. $\frac{3}{7}$ |
It is given that $A$ and $B$ are such that $P(A) = \frac{1}{4}$,$P(A|B) = \frac{1}{2}$,and $P(B|A) = \frac{2}{3}$. Then $P(B) = $?
MediumAIEEE 2008
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If $\overline{E}$ and $\overline{F}$ are the complementary events of events $E$ and $F$ respectively and if $0 < P(F) < 1$,then
Let $A$ and $B$ be two independent events such that $P(A) + P(B) = \frac{3}{4}$ and $P(\overline{A} | B) = \frac{2}{5}$. Then,$P(A \cap B)$ is -
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