CUET Mathematics 2022 10 Aug Shift 1 PYQs

A doctor is to visit a patient. It is known that the probabilities that he will come by train, bus, scooter or by other means of transport are respectively $\frac{3}{10}, \frac{1}{5}, \frac{1}{10}$ and $\frac{2}{5}$. The probabilities that he will be late are $\frac{1}{4}, \frac{1}{3}$ and $\frac{1}{12}$, if he comes by train, bus and scooter respectively, but if he comes by other means of transport, then he will not be late. When he arrives, he arrives late.

The probability that he comes by bus is:

If X is a random variable and a, b are real numbers, then which of the following statements are correct?

(A) $E[aX+b] = a E(X) + b$

(B) $Var (aX + b) = a^2 Var (X) + b$

(C) $Var (aX + b) = a Var (X)$

(D) $Var (X) = E(X^2) - [E(X)]^2$

Choose the correct answer from the options given below:

A coin is tossed K times. If the probability of getting $3$ heads is equal to the probability of getting $7$ heads, then the probability of getting $8$ tails is :