Question

A letter is taken out at random from the word 'ASSISTANT and another is taken-out from the word 'STATISTICS'. The chance that the two selected letters are identical, is

• A. $ 19/45 $
• B. $ 19/90 $
• C. $ 89/90 $
• D. $ 1/90 $

Answer 1

Answer: (B)

The letters of the word 'ASSISTANT' are A, A, I, N, S, S, S, T, T and the letters of the word 'STATISTICS' are A, C, I, I, S, S, S, T, T, T
Case (i) W letter is taken from each of the word, then its probability $ P(A)=\frac{^{2}{{C}_{1}}}{^{9}{{C}_{1}}}\times \frac{^{1}{{C}_{1}}}{^{10}{{C}_{1}}}=\frac{2}{90} $
Case (ii) 'I' letter is taken from each of the word, then its probability $ P(I)=\frac{^{1}{{C}_{1}}}{^{9}{{C}_{1}}}\times \frac{^{2}{{C}_{1}}}{^{10}{{C}_{1}}}=\frac{2}{90} $
Case (iii) 'S' letter is taken from each of the word, then its probability
$ P(S)=\frac{^{3}{{C}_{1}}}{^{9}{{C}_{1}}}\times \frac{^{3}{{C}_{1}}}{^{10}{{C}_{1}}}=\frac{9}{90} $
Case (iv) 'T' letter is taken from each of the word, then its probability
$ P(T)=\frac{^{2}{{C}_{1}}}{^{9}{{C}_{1}}}\times \frac{^{3}{{C}_{1}}}{^{10}{{C}_{1}}}=\frac{6}{90} $
Combined probability
$=\frac{2}{90}+\frac{2}{90}+\frac{9}{90}+\frac{6}{90}=\frac{19}{90} $