≠ φ and B ∩ D ≠ φ . Thus, the pairs of events, (A, C), (A, D), (B, C), (B, D) are not mutually exclusive events. Also C ∩ D = φ and so C and D are mutually exclusive events. Example A coin is tossed three times, consider the following events.
A: ‘No head appears’, B: ‘Exactly one head appears’ and C: ‘Atleast two heads appear’. Do they form a set of mutually exclusive and exhaustive events? Solution The sample space of the experiment is S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT} and A = {TTT}, B = {HTT, THT, TTH}, C = {HHT, HTH, THH, HHH} Now A ∪ B ∪ C = {TTT, HTT, THT, TTH, HHT, HTH, THH, HHH} = S Therefore, A, B and C are exhaustive events. Also, A ∩ B = φ , A ∩ C = φ and B ∩ C = φ Therefore, the events are pair-wise disjoint, i.e., they are mutually exclusive.
Hence, A, B and C form a set of mutually exclusive and exhaustive events. PROBABILITY EXERCISE . . A die is rolled.
Let E be the event “die shows ” and F be the event “die shows even number”. Are E and F mutually exclusive? . A die is thrown.
Describe the following events: A: a number less than B: a number greater than (iii) C: a multiple of (iv) D: a number less than (v) E: an even number greater than (vi) F: a number not less than Also find A ∪ B, A ∩ B, B ∪ C, E ∩ F, D ∩ E, A – C, D – E, E ∩ F ′ , F ′ . 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 , B: occurs on either die C: the sum is at least and a multiple of . Which pairs of these events are mutually exclusive?
. Three coins are