A bag contains $3$ red and $7$ black balls, two balls are taken out at random, without replacement. If the first ball taken out is red, then what is the probability that the second taken out ball is also red
$\frac{1}{{10}}$
$\frac{1}{{15}}$
$\frac{3}{{10}}$
$\frac{2}{{21}}$
An experiment consists of tossing a coin and then throwing it second time if a head occurs. If a tail occurs on the first toss, then a die is rolled once. Find the sample space.
In a class of $60$ students, $40$ opted for $NCC,\,30$ opted for $NSS$ and $20$ opted for both $NCC$ and $NSS.$ If one of these students is selected at random, then the probability that the student selected has opted neither for $NCC$ nor for $NSS$ is
Let $E$ and $F$ be two independent events. The probability that both $E$ and $F$ happen is $\frac{1}{12}$ and the probability that neither $E$ nor $F$ happens is $\frac{1}{2}$ , then a value of $\frac{{P(E)}}{{P\left( F \right)}}$ is
Three coins are tossed once. Find the probability of getting atmost two tails.
A die has two faces each with number $^{\prime}1^{\prime}$ , three faces each with number $^{\prime}2^{\prime}$ and one face with number $^{\prime}3^{\prime}$. If die is rolled once, determine $P (2)$.