A problem in Mathematics is given to two students X and Y whose chances of solving it are $\frac{1}{3}$ and $\frac{1}{4}$ respectively. The probability that only X solves the problem, is:

Nitin has taken the subjects mathematics, physics and chemistry. The probability of him getting grade A in these subjects are respectively 0.2, 0.3 and 0.9. Getting grades in different subjects are regarded as independent events. The probability of getting A grade by him, either in mathematics or physics, is

When the doctor arrives late, what is the probability that he comes by bike?

If A and B are two independent events with $P(A) = \frac{1}{5}$ and $P(B) = \frac{1}{3}$, then $P(A'/B)$ is:

There are $6$ cards numbered $1$ to $6$, one number on one card. Two cards are drawn at random without replacement. Let X denote the sum of the numbers on the two cards drawn. Then $\mathrm{P}(\mathrm{X}>3)$ is :

A shopkeeper sells three types of flower seeds $A_1, A_2, A_3$. They are sold as a mixture where the proportions are 4 : 4 : 2 respectively. The germination rates of the three types of seeds are 45%, 60% and 35% respectively. Calculate the probability in the following cases.

The probability that seed is of type $A_1$ given that seed doesn't germinate.

In Binomial distribution with parameters $n = 100$ and p, Variance of distribution is maximum when p is equal to :