Examples

Chapter 14 Class 11 Probability
Serial order wise

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class

### Transcript

Example 8 A coin is tossed three times, consider the following events. A: ‘No head appears’, B: ‘Exactly one head appears’ and C: ‘At least two heads appear’. Do they form a set of mutually exclusive and exhaustive events? If 3 coins are tossed , possible outcomes are S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT} A: no head appear Hence only tail appear in all 3 times So A = {TTT} B: exactly one head appear B = {HTT, THT, TTH} C: at least two heads appear C = {HHT, HTH, THH, HHH} Thus, A = {TTT} B = {HTT, THT, TTH} C = {HHT, HTH, THH, HHH} A ∪ B ∪ C = {TTT, HTT, THT, TTH, HHT, HTH, THH, HHH} = S Hence A, B and C are exhaustive events. Checking Mutually Exclusive A ∩ B = {TTT} ∩ {HTT, THT, TTH} = 𝜙 There is no common elements in A & B So, A & B are mutually exclusive A ∩ C = {TTT} ∩ {HHT, HTH, THH, HHH} = 𝜙 There is no common elements in A & C Hence A & C are mutually exclusive B ∩ C = {HTT, THT, TTH} ∩ {HHT, HTH, THH, HHH} = 𝜙 There is no common element in B & C Hence B & C are mutually exclusive Since A & B, A & C, B & C are mutually exclusive Hence A, B and C are mutually exclusive Hence, A, B and C form a set of mutually exclusive and exhaustive events.

#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.