Conditional Probability and Independent Events

Given that,  $P\left(A\right|B)=0.3$, $P\left(B\right|A)=0.2$ and $A$ and $B$ are independent events, then $P\left(A\right)$ is.

On throwing the single die, then the event of getting odd number or even number are _____ event.

If $P\left(A\right)=0.2$ and $P\left(A\cap B\right)=0.11$, then find $P\left(B|A\right)$.

If $P\left(B\right)=0.3$ and $P\left(A\cap B\right)=0.12$, then find $P\left(A|B\right)$.

If $2P\left(A\right)=P\left(B\right)=\frac{4}{13}$ and $P\left(A|B\right)=\frac{2}{5}$, then find $P\left(A\cup B\right)$.

If $P\left(A\right)=0.7, P\left(B\right)=0.4$ and $P\left(B|A\right)=0.4$, then find $P\left(A\cap B\right)+P\left(A|B\right)+P\left(A\cup B\right)$.

A die is thrown three times, Find $P\left(E|F\right)$, If $E$ and $F$ are defined as follows:

$E:4$ appears on the third toss,

$F:4$ and $3$ appears respectively on first two tosses

A black and a red dice are rolled. Find the conditional probability of obtaining a sum greater than $8$, given that the black die resulted in  $\mathrm{}5$.

Given that the two numbers appearing on throwing the two dice are different. Find the probability of the event ‘the sum of numbers on two dice is $6$’.

If $P\left(A\cap B\right)=\frac{1}{7}, P\left(B\right)=\frac{1}{2}$, then $P\left(A|B\right)$ is

If $P\left(A\right)=\frac{1}{2}, P\left(B\right)=0$, then $P\left(A|B\right)$ is

Given that the two numbers appearing on throwing the two dice are different. Find the probability of the event ‘the sum of numbers on the dice is $\mathrm{}4$’.

A black and a red dice are rolled. Find the conditional probability of obtaining a sum greater than $\mathrm{}9$, given that the black die resulted in  $\mathrm{}5$.

A die is thrown three times, Find $P\left(E|F\right)$, If $E$ and $F$ are defined as follows:

$E:4$ appears on the third toss,

$F:6$ and $\mathrm{}5\mathrm{}$ appears respectively on first two tosses

Two coins are tossed once, where $E$: tail appears on one coin, $F$: one coin shows head. Determine $P\left(E|F\right)$.

If $P\left(A\right)=0.8, P\left(B\right)=0.5$ and $P\left(B|A\right)=0.4$, then find $P\left(A\cap B\right)+P\left(A|B\right)+P\left(A\cup B\right)$.

If $2P\left(A\right)=P\left(B\right)=\frac{5}{13}$ and $P\left(A|B\right)=\frac{2}{5}$, then find $P\left(A\cup B\right)$.

If $P\left(B\right)=0.5$ and $P\left(A\cap B\right)=0.32$, then find $P\left(A|B\right)$.

Given that $E$ and $F$ are events such that $P\left(E\right)=0.6, P\left(F\right)=0.3$ and $P\left(E\cap F\right)=0.2$, find $P\left(E|F\right)+P\left(F|E\right)$.

If $P(A\cap B)=0.2, P\left(B\right)=0.5$, then find the value of  $P\left(A|B\right)$.