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Page 1 of 9, Exercise 16.2, Question 1:, A die is rolled. Let E be the event "die shows 4" and F be the event "die shows even, number". Are E and F mutually exclusive?, Answer, When a die is rolled, the sample space is given by, S = {1, 2, 3, 4, 5, 6}, Accordingly, E =, {4} and F = {2, 4, 6}, It is observed that EN F = {4} # 0, %3D, Therefore, E and F are not mutually exclusive events., Question 2:, A die is thrown. Describe the following events:, (i) A: a number less than 7 (ii) B: a number greater than 7 (iii) C: a multiple of 3, (iv) D: a number less than 4 (v) E: an even number greater than 4 (vi) F: a number not, less than 3, Also find AUB, AnB, BUC,EnF,DNE, A-C, D-E, EOF,F', Answer, When a die is thrown, the sample space is given by S = {1, 2, 3, 4, 5, 6}., Accordingly:, (i) A = {1, 2, 3, 4, 5, 6}, (ii) B, = O, (iii) C = {3, 6}, %3D, (iv) D = {1, 2, 3}

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Page 2 of 9, Class XI, Chapter 16 Probability, Maths, (v) E = {6}, %3D, (vi) F = {3, 4, 5, 6}, AUB 3D {1, 2, 3, 4, 5, 6}, АПВ %3D Ф, BUC = {3, 6}, E N F = {6}, DNE =0, A -C = {1, 2, 4, 5}, %3D, D - E = {1, 2, 3}, F' = {1,2}, EnF'= ¢, %3D, Question 3:, An experiment involves rolling a pair of dice and recording the numbers that come up., Describe the following events:, A: the sum is greater than 8, B: 2 occurs on either die, C: The sum is at least 7 and a multiple of 3., Which pairs of these events are mutually exclusive?, Answer, When a pair of dice is rolled, the sample space is given by, S= {(x,y): x,y = 1,2,3,4,5,6}, (1.1). (1.2). (1.3). (1.4). (1.5). (1.6), |(2,1). (2.2). (2.3). (2.4). (2,5). (2.6), |(3,1). (3,2). (3,3). (3,4). (3.5). (3.6)|, |(4.1). (4.2). (4.3). (4.4). (4.5). (4,6), |(5.1). (5.2). (5.3). (5.4). (5.5). (5.6), |(6.1). (6,2). (6,3). (6,4). (6,5). (6.6)], Accordingly,, A = {(3,6).(4.5).(4,6).(5.4).(5.5).(5.6).(6.3).(6,4).(6,5).(6,6)}, B = {(2.1).(2.2).(2.3).(2.4).(2.5).(2.6).(1.2).(3,2).(4.2).(5.2).(6. 2)}, C ={(3,6).(4,5).(5,4).(6.3).(6,6)}, %3D, It is observed that, ANB =0

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Page 3 of 9, Class XI, Chapter 16 -, Probability, Maths, BN C =0, CnA = {(3,6).(4,5),(5,4).(6,3).(6,6)}#ø, Hence, events A and B and events B and C are mutually exclusive., Question 4:, Three coins are tossed once. Let A denote the event 'three heads show", B denote the, event "two heads and one tail show". C denote the event "three tails show" and D, denote the event 'a head shows on the first coin". Which events are, (i) mutually exclusive? (ii) simple? (iii) compound?, Answer, When three coins are tossed, the sample space is given by, S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}, Accordingly,, A =, {HHH}, В %3D {ННТ, нтH, тнн}, C = {TTT}, D %3D {HНH, Нт, нтн, нтт}, We now observe that, ANB =0, A n C =0, A ND =, {HHH} + 0, BNC =0, B ND =, {HHT, {HTH} #, CND = 0, (i) Event A and B; event A and C; event B and C; and event C and D are all mutually, exclusive., (ii) If an event has only one sample point of a sample space, it is called a simple event., Thus, A and C are simple events., (iii) If an event has more than one sample point of a sample space, it is called a, compound event. Thus, B and D are compound events., Question 5:, Three coins are tossed. Describe, (i) Two events which are mutually exclusive., (ii) Three events which are mutually exclusive and exhaustive., (ii) Two events, which are not mutually exclusive.

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Page 4 of 9, Maths, Class XI, Chapter 16 Probability, (iv) Two events which are mutually exclusive but not exhaustive., (v) Three events which are mutually exclusive but not exhaustive., Answer, When three coins are tossed, the sample space is given by, {нНН, ННТ, нтн, нтт, тHH, THT, TTH, TIT}, S =, (i) Two events that are mutually exclusive can be, A: getting no heads and B: getting no tails, This is because sets A =, {TTT} and B =, {HHH} are disjoint., (ii) Three events that are mutually exclusive and exhaustive can be, A: getting no heads, B: getting exactly one head, C: getting at least two heads, i.e.,, = {TTT}, B = {HTT, THT, TTH}, С %3D {ННН, ННт, нтн, тHн}, A =, %3D, This is because A N B = BNC = CNA = Dand A UBUC = S, (iii) Two events that are not mutually exclusive can be, A: getting three heads, B: getting at least 2 heads, i.e.,, A =, {HHH}, {нНн, нНТ, нтн, тну, B =, This is because A N B =, {HHH} # 0, (iv) Two events which are mutually exclusive but not exhaustive can be, A: getting exactly one head, B: getting exactly one tail, That is, A =, {HTT, THT, TTH}, В %3D {ННТ, НTH, тнн), It is because, ANB =0, but Au B # S, %3D, (v) Three events that are mutually exclusive but not exhaustive can be, A: getting exactly three heads

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Page 5 of 9, Class XI, Chapter 16 Probability, Maths, B: getting one head and two tails, C: getting one tail and two heads, i.e.,, A =, {HHH}, B = {HTT, THT, TTH}, C = {HHT, HTH, THH}, This is because A N B = B NC = CNA = 0, but A UBUC + S, Question 6:, Two dice are thrown. The events A, B and C are as follows:, A: getting an even number on the first die., B: getting an odd number on the first die., C: getting the sum of the numbers on the dice < 5, Describe the events, (i) A' (ii) not B (iii) A or B, (iv) A and B (v) A but not C (vi) B or C, (vii) B and C (viii) AnB'nC', Answer, When two dice are thrown, the sample space is given by