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Question
Solve the following:
A letter is taken at random from the letters of the word 'ASSISTANT' and another letter is taken at random from the letters of the word 'STATISTICS'. Find the probability that the selected letters are the same
Solution
Word ASSISTANT has 2A, I, N, 3S, 2T and
word STATISTICS has A, C, 2I, 3S, 3T.
C and N are uncommon letters.
In words ASSISTANT, there are 9 letters out of which 2 letters are ‘A’ and in word STATISTICS, there are 10 letters, out of which 1 letter is A.
∴ Probability of choosing A from both the letters
= `(""^2"C"_1)/(""^9"C"_1) xx (""^1"C"_1)/(""^10"C"_1)`
= `2/9 xx 1/10`
= `1/45`
Similarly,
Probability of choosing I from both the letters
= `(""^1"C"_1)/(""^9"C"_1) xx (""^2"C"_1)/(""^10"C"_1)`
= `1/9xx2/10`
= `1/45`
Probability of choosing S from both the letters
= `(""^3"C"_1)/(""^9"C"_1) xx (""^3"C"_1)/(""^10"C"_1)`
= `3/9xx3/10`
= `1/10`
Probability of choosing T from both the letters
= `(""^2"C"_1)/(""^9"C"_1) xx (""^3"C"_1)/(""^10"C"_1)`
= `2/9 xx 3/10`
= `1/15`
∴ Required probability = `1/45 + 1/45 + 1/10 + 1/15`
= `19/90`
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