Q5 of 134 Page 32

Three coins are tossed. Describe

(i) two events A and B which are mutually exclusive.


(ii) three events A, B and C which are mutually exclusive and exhaustive.


(iii) two events A and B which are not mutually exclusive.


(iv) two events A and B which are mutually exclusive but not exhaustive.

When three coins are tossed, then the sample space is


S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}


Now, The subparts are:


(i) The two events which are mutually exclusive are when,


A: getting no tails


B: getting no heads


Then, A = {HHH} and B = {TTT}


SO, The intersection of this set will be null.


Or, The sets are disjoint.


(ii) Three events which are mutually exclusive and exhaustive are:


A: getting no heads


B: getting exactly one head


C:getting at least two head


So, A = {TTT} B = {TTH, THT, HTT} and C = {HHH, HHT, HTH, THH}


Since,


(iii) The two events that are not mutually exclusive are:


A:getting three heads


B:getting at least 2 heads


So, A = {HHH} B = {HHH, HHT, HTH, THH}


Since


(iv) The two events which are mutually exclusive but not exhaustive are:


A:getting exactly one head


B: getting exactly one tail


So, A = {HTT, THT, TTH} and B = {HHT, HTH, THH}


It is because


More from this chapter

All 134 →
3

Three coins are tossed once. Describe the following events associated with this random experiment:

A = Getting three heads, B = Getting two heads and one tail, C = Getting three tails, D = Getting a head on the first coin.


(i) Which pairs of events are mutually exclusive?


(ii) Which events are elementary events?


(iii) Which events are compound events?

 4

In a single throw of a die describe the following events:

(i) A = Getting a number less than 7


(ii) B = Getting a number greater than 7


(iii) C = Getting a multiple of 3


(iv) D = Getting a number less than 4


(v) E = Getting an even number greater than 4.


(vi) F = Getting a number not less than 3.


Also, find A ∪ B, A ∩ B, B ∩ C, E ∩ F, D ∩ F and .

 6

A die is thrown twice. Each time the number appearing on it is recorded. Describe the following events:

(i) A = Both numbers are odd.


(ii) B = Both numbers are even


(iii) C = sum of the numbers is less than 6.


Also, find A ∪ B, A ∩ B, A ∪ C, A ∩ C. Which pairs of events are mutually exclusive.

 7

Two dice are thrown. The events A, B, C, D, E and F are describes 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


(c) A and C are mutually exclusive 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 are mutually exclusive and exhaustive events