The probability that India wins the toss is $3/4$. If it wins the toss,the probability of winning the match is $4/5$,otherwise it is $1/2$. Find the probability that India wins the match.

$A$ purse contains $4$ copper coins and $3$ silver coins,the second purse contains $6$ copper coins and $2$ silver coins. If a coin is drawn out of one of these purses,then the probability that it is a copper coin is :-

If $A_i$ $(i=1, 2, 3, \ldots, n)$ are $n$ independent events with $P(A_i) = \frac{1}{1+i}$ for each $i$,then the probability that none of $A_i$ occurs is

For independent events $A$ and $B$,$P(A) = \frac{1}{3}$,$P(A \cup B) = \frac{2}{5}$,and $P(B) = p$. Find the value of $p$.

$A$ bag contains $10$ white and $15$ red balls. If two balls are drawn one after another,what is the probability that the first ball is red and the second ball is white?

Two marbles are drawn in succession from a box containing $10$ red,$30$ white,$20$ blue and $15$ orange marbles,with replacement being made after each drawing. Then the probability,that the first drawn marble is red and the second drawn marble is white,is