(b) Events A, B and C of S which are mutually exclusive and exhaustive.

(c) Events A and B of S which are not mutually exclusive.

Two dice are thrown. The events A, B, C, D, E, F are as follows:

A : Getting an even number on the first die.

B : Getting an odd number on the first die.

C : Getting sum of numbers on the two dice as ≤ 5.

D : Getting the sum of two numbers on the dice greater than 5 but less than 10.

E : Getting sum of numbers on the two dice as ≥ 10.

F : Getting an odd number on exactly one of the dice.

Describe events (i) A' (ii) B' (iii) E' (iv) A or B (v) A and B (vi) B or C (vii) B and C (viii) A and E (ix) A or F (x) A and F.

Two dice are thrown. The events A, B, C are as follows:

A : Getting an even number on the first die.

B : Getting an odd number on the first die.

C : Getting the sum of the numbers on the dice ≤ 5

Describe the events:

(i) A' (ii) not B (iii) A or B

(iv) A and B (v) A but not C (vi) B or C

(vii) B and C (viii) A ∩ B' ∩ C' (ix) A ∩ B ∩ C'

The numbers 1, 2, 3, 4 are written separately on four slips of paper. The slips are then put in a box and mixed thoroughly.

Two slips are then drawn from the box, one after the other, without replacement. Events A, B, C and D are described as follows:

A : The number on the first slip is greater than the number on the second slip.

B : The number on the second slip is greater than 2.

C : The sum of the numbers on the two slips is 6 or 7.

D : The number on the second slip is twice the number on the first slip.

E : The number on the first slip is 3 times that on the second slip.

Find: (a) Which pairs of events are mutually exclusive?

(b) Which of the events are simple events?

(c) Which of the events are compound events?

425. The probability of an event A happening is given by:
          
Find: (i) odds in favour (ii) odds against the happening of the event.

If  is the probability of an event, what is the probability of the event 'not A'.