If $A$ and $B$ are two independent events such that $P(A^{\prime}) = 0.75$,$P(A \cup B) = 0.65$ and $P(B) = p$,then the value of $p$ is

$A$ fair die is tossed until a six is obtained. Let $X$ be the number of required tosses,then the conditional probability $P(X \geq 5 \mid X > 2)$ is:

$A$ die is thrown. If $E$ is the event 'the number appearing is a multiple of $3$' and $F$ is the event 'the number appearing is even',then find whether $E$ and $F$ are independent?

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 English newspaper,find the probability that she reads Hindi newspaper.

Let $B(\alpha, \beta, \gamma)$ represent that a bag $B$ contains $\alpha$ red balls,$\beta$ green balls,and $\gamma$ blue balls. Given $B_1(2, 3, 2)$,$B_2(3, 2, 2)$,$B_3(2, 2, 3)$. $A$ die is rolled. If the die shows $2, 3,$ or $5$,a ball is drawn from bag $B_1$. If the die shows $4$ or $6$,a ball is drawn from bag $B_2$. If the die shows $1$,a ball is drawn from bag $B_3$. Find the probability of drawing a green ball.

Three coins are tossed. If one of them shows tail,then the probability that all three coins show tail,is