Ex 16.2, 5
Three coins are tossed. Describe
(ii) Three events which are mutually exclusive and exhaustive.
S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}
Let A be the event getting exactly two tail comes
A = {HTT, THT, TTH}
Let B be the event getting at least two head
B = {HHT, HTH, THH, HHH}
Let C be the event getting only tail
C = {TTT}
A ∩ B = {HTT, THT, TTH} ∩ {HHT, HTH, THH, HHH}
= 𝜙
Since no element is common in A & B
Hence, A & B are mutually exclusive
B ∩ C = {HHT, HTH, THH, HHH} ∩ {TTT}
= 𝜙
Since no element is common in B & C
Hence, B & C are mutually exclusive
A ∩ C = {HHT, THT, TTH} ∩ {TTT}
= 𝜙
Since no element is common in A & C
Hence, A & C are mutually exclusive
Since A & B, A & C, B & C are mutually exclusive
Hence A, B and C are mutually exclusive
Also,
A ∪ B ∪ C = {HTT, THT, TTH, HHT, HTH, THH, HHH}
= S
Hence A, B & C are exhaustive events

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.

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