Atul and Bhuvan play a game where each is asked to select a number from 1 to 9. If the two numbers same, both win a prize. The probability that they will not win a prize in a single trial is:
Total number of ways in which both can select a number each: = 9 × 9 = 81 Total number of ways in which both can select a same number so that they both can win: = 9 ways [They both can select {(1,1), (2,2), (3,3), (4,4), (5,5), (9,6), (7,7) (8,8) (9,9)}] Probability that they win the prize: = Favourable Cases/Total Cases = 9/81 = 1/9 Probability that they do not win a prize = 1 - 1/9 = 8/9.
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