1.

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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