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Exhaustive Events

A batsman is ...

Question

A batsman is going to face a delivery. Following events are described.
X = {He will get out}
Y = {He will score one or more runs on this delivery}
Z = {He will not score any run on this delivery}
Events X , Y and Z are exhaustive events.

True

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False

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Solution

The correct option is A True
Just think what all the possibilities are when a batsman is facing a delivery from a bowler. Either he gets out, plays a dot ball or score one or more runs. There is no other possibility. These events cover everything that can happen on that delivery. Yeah you are right. They are exhaustive.

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

A = Getting an even number on the first die.

B = Getting an odd number on the first die.

C = Getting at most 5 as sum of the numbers on the two dice.

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

E = Getting at least 10 as the sum of the numbers on the dice.

F = Getting an odd number on one of the dice.

(i) Describe the following events : A and B, B or C, B and C, A and E, A or F, A and F

(ii) State true or false :

(a) A and B are mutually exclusive.

(b) A and B are mutually exclusive and exhaustive events.

(d) C and D are mutually exclusive and exhaustive events.

(e) C, D and E are mutually exclusive and exhaustive events.

(f) A' and B' are mutually exclusive events.

(g) A, B, F arc mutually exclusive and exhaustive events.

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