Out of 100 students, two sections of 40 and 60 are formed. If you and your friend are among the hundred students, what is the probability that

(a) you both enter the same section?

(b) you both enter different sections? 

Check whether the following probabilities are correctly defined:

(i) P (A) = 0.45,           P(B) = 0.65,       P (A ∩ B) = 0.55

(ii) P (A) = 0.6,            P (B) = 0.7,        P (A ∪ B) = 0.8

Arin has to visit at random three of his friends A, B and C over a week-end. What is the probability that he visits:

(a) B before C                (b) B before C and C before A

(c) C first                       (d) A just before B

(e) A either first or last?

If 4-digit numbers greater than 5,000 are randomly formed from digits 0, 1, 3, 5 and 7. What is the probability of forming a number divisible by 5 when:(i) the digits are repeated? (ii) the repetition of digits is not allowed?

A, B, C are three mutually exclusive and exhaustive events of a random experiment. Find the values of P(A), P(B) and P(C), given that 

If A and B are two mutually exclusive events, then prove that P(A ∪ B) = P(A) + P(B)

600.  If A and B arc any two events, then prove that:
(a)     (b)