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Ex 16.2, 5 - Three coins are tossed. Describe (i) Two events - Ex 16.2

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  1. Chapter 16 Class 11 Probability
  2. Serial order wise
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Ex16.2, 5 Three coins are tossed. Describe โ€ข Two events which are mutually exclusive. Since 3 coins are tossed , possible outcomes are S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT} Two events which are mutually exclusive Let A be the event getting only head A = {HHH} Let B be the event getting only tail B = {TTT} So, A โˆฉ B = ๐œ™ Since no element is common in A & B Hence A & B are mutually exclusive Ex16.2, 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 โˆฉ B = {HTT, THT, TTH} โˆฉ {HHT, HTH, THH, HHH} = ๐œ™ Since no element is common in A & B Hence A & B are mutually exclusive B โˆฉ C = {HHT, HTH, THH, HHH} โˆฉ {TTT} = ๐œ™ Since no element is common in B & C Hence B & C are mutually exclusive A โˆฉ C = {HHT, THT, TTH} โˆฉ {TTT} = ๐œ™ 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 โˆช B โˆช C = {HTT, THT, TTH, HHT, HTH, THH, HHH} = S Hence A, B & C are exhaustive events Ex16.2, 5 Three coins are tossed. Describe (iii) Two events, which are not mutually exclusive. S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT} Let A be the event getting at least two head A = {HHH, HHT, HTH, THH} Let B be the event getting only head B = {HHH} A โˆฉ B = {HHH} โ‰  ๐œ™ Since there is a common element in A & B Hence A & B are not mutually exclusive Ex16.2, 5 Three coins are tossed. Describe (iv) Two events which are mutually exclusive but not exhaustive. Two events which are mutually exclusive but not exhaustive Let A be the event getting only Head A = {HHH} Let B be the event getting only tail B = {TTT} A โˆฉ B = {HHH} โˆฉ {TTT} = ๐œ™ Since no element is common in A & B Hence A & B are mutually exclusive But A โˆช B = {HHH} โˆช {TTT} = {(HHH), (TTT)} โ‰  S Since A โˆช B โ‰  S They are not exhaustive events Ex16.2, 5 Three coins are tossed. Describe (v) Three events which are mutually exclusive but not exhaustive. Three event which are mutually exclusive but not exhaustive Let A be the event getting only head A = {HHH} Let B be the event getting only tail B = {TTT} Let C be the event getting exactly two tails C = {HHT, HTH, THH} A โˆฉ B = {HHH} โˆฉ {TTT} = ๐œ™ B โˆฉ C = {TTT} โˆฉ {HTT, TH, THT} = ๐œ™ & A โˆฉ C = {HHH} โˆฉ {HTT, TTH ,THT} = ๐œ™ A โˆฉ B = ๐œ™ , A โˆฉ C = ๐œ™ & B โˆฉ C = ๐œ™ Therefore the event are pair wise disjoint i.e. they are mutually exclusive But, A โˆช B โˆช C = {HHH, TTT, HTT, THT, TTH} โ‰  S Since A โˆช B โˆช C โ‰  S Hence A, B & C are not exhaustive Hence A, B & C are mutually exclusive but not exhaustive

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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