ProbabilityHardBloom L3
Question
An unbiased coin is tossed. If the result is head, a pair of unbaised dice is rolled and the number obtained by adding the numbers on the two faces is noted. If the result is a tail, card is drawn from a well shuffled pack of eleven cards numbered $2,3,4$, $5,\ldots..,11,12$ is picked and the number on the card is noted. Then the probability that the noted number is 7 or 8 is equal to
Options
A.$\frac{195}{792}$
B.$\frac{185}{792}$
C.$\frac{191}{792}$
D.$\frac{193}{792}$
Solution
Sol. [Key Concept: Coin toss branching (head→…): condition on the first outcome.]
$$P = \frac{1}{2}\left( \frac{6 + 5}{36} + \frac{2}{11} \right) = \frac{193}{792}$$
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