

InterviewSolution
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If four dice are rolled, find the number of possible outcomes in which atleast one die shows 2. |
Answer» When a die is rolled number of possible outcomes is selecting an event from 6 events = 6C1 When four dice are rolled number of possible outcomes = 6C1 x 6C1 x 6C1 x 6C1 When a die is rolled number of possible outcomes in which ‘2’ does not appear is selecting an event from 5 events = 5C1 When four dice are rolled number of possible outcomes in which 2 does not appear = 5C1 x 5C2 x 5C3 x 5C4 Therefore the number of possible outcomes in which atleast one die shows 2 = 6C1 x 6C1 x 6C1 x 6C1 – 5C1 x 5C2 x 5C3 x 5C4 = 6 x 6 x 6 x 6 – 5 x 5 x 5 x 5 = 1296 – 625 = 671 Note: when two dice are rolled number of possible outcomes is 36 and the number of possible outcomes in which 2 doesn’t appear = 25. When two dice are rolled the number of possible outcomes in which atleast one die shows 2 = 36 – 25 = 11. Use the sample space, S = {(1, 1), (1, 2), … (6, 6)}. |
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