Question
A game consists of tossing three coins once and then
rolling two dice. Find the probability of getting at least two heads in the coin toss and a sum equal to 6 on the dice.Solution
For tossing 3 coins: Total number of possible outcomes = 23 = 8 Favourable outcomes for at least two heads = HHT, HTH, THH, HHH = 4 outcomes So, probability = (4/8) = (1/2) For rolling 2 dice: Total number of possible outcomes = 6 × 6 = 36 Number of favourable outcomes = 5 [(1,5), (2,4), (3,3), (4,2), (5,1)] So, Probability of getting a sum equal to 6 while rolling 2 dice = (5/36) Required probability = (1/2) × (5/36) = 5/72
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