ProbabilityHardBloom L3
Question
A letter is chosen at random out of 'ASSININE' and one out of 'ASSASSIN'. Find the probability that the same letter is chosen on both occasions. (A) 7/16 (B) 7/32 (C) 5/16 (D) 9/32
Options
A.7/16
B.7/32
C.5/16
D.9/32
Solution
Sol. [Key Concept: Sum over the common letters: $P(letter\ in\ word\ 1) \times \ P(same\ letter\ in\ word\ 2)$.] $P = \frac{\begin{matrix} \text{~}\text{both 'a' both 's' both '}\text{~}i\text{~}\text{' both '}\text{~}n\text{~}\text{'}\text{~} \\ 1 \times 2 + 2 \times 4 + 2 \times 1 + 2 \times 1 \end{matrix}}{8 \times 8} = \frac{14}{64} = \frac{7}{32}$
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