If A and B are two independent events such that, P(A) = 0.4 and P\((A\cup B)\) = 0.9. Find P(B).

Suppose a fair die is rolled. Find the probability of getting (i) an even number (ii) multiple of three.

A main road in a City has 4 crossroads with traffic lights. Each traffic light opens or closes the traffic with the probability of 0.4 and 0.6 respectively. Determine the probability of
(i) a car crossing the first crossroad without stopping
(ii) a car crossing first two crossroads without stopping
(iii) a car crossing all the crossroads, stopping at third cross.
(iv) a car crossing all the crossroads, stopping at exactly one cross.

Three letters are written to three different persons and addresses on three envelopes are also written. Without looking at the addresses, what is the probability that (i) exactly one letter goes to the right envelopes (ii) none of the letters go into the right envelopes?

Let the matrix M = \(\left[ \begin{matrix} x & y \\ z & 1 \end{matrix} \right] \), If x,y and z are chosen at random from the set {1, 2,3, } and repetition is allowed (i.e., x = y = z ), what is the probability that the given matrix M is a singular matrix?

A town has 2 fire engines operating independently. The probability that a fire engine is available when needed is 0.96.
(i) What is the probability that a fire engine is available when needed?
(ii) What is the probability that neither is available when needed?

For a sports meet, a winners’ stand comprising of three wooden blocks is in the form as shown in figure. There are six different colours available to choose from and three of the wooden blocks is to be painted such that no two of them has the same colour. Find the probability that the smallest block is to be painted in red, where red is one of the six colours.

Five mangoes and 4 apples are in a box. If two fruits are chosen at random, find the probability that (i) one is a mango and the other is an apple (ii) both are of the same variety.

An integer is chosen at random from the first 100 positive integers. What is the probability that the integer chosen is a prime or multiple of 8?

(i) The odds that the event A occurs is 5 to 7, find P(A)..
(ii) Suppose \(P(B)=\frac{2}{5},\) Express the odds that the event B occurs.