A letter is takenout at random from 'ASSISTANT' and another is taken out from 'STATISTICS'. The probability that they are the same letter is :
Solution
Correct Answer: Option B
\(ASSISTANT\rightarrow AAINSSSTT\)
\(STATISTICS\rightarrow ACIISSSTTT\)
Here N and C are not common and same letters can be A, I, S, T. Therefore
Probability of choosing A = \(\frac{2_{C_1}}{9_{C_1}}\times\frac{1_{C_1}}{{10}_{C_1}}\) = 1/45
Probability of choosing I = \(\frac1{9_{C_1}}\times\frac{2_{C_1}}{{10}_{C_1}}\) = 1/45
Probability of choosing S = \(\frac{3_{C_1}}{9_{C_1}}\times\frac{3_{C_1}}{{10}_{C_1}}\) = 1/10
Probability of choosing T = \(\frac{2_{C_1}}{9_{C_1}}\times\frac{3_{C_1}}{{10}_{C_1}}\) = 1/15
Hence, Required probability = \(\frac1{45}+\frac1{45}+\frac1{10}+\frac1{15}=\;\frac{19}{90}\)
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