Question

Suppose that a person chooses a letter at random from "r e s e r v e" and then chooses one at random from "vertical". what is the probability that the same letter is chosen

Answer 1

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Total number of letters=15
Number of same letters in both=12

Probability of getting same letter=12/15

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Answer 2

In the word "reverse", total number of letters = 7

In the word "vertical", total number of letters = 8

common letters are = r, e, v.

probability of choosing "r" in "reverse" = 2/7 and in "vertical" = 1/8

probability of choosing "e" in "reverse" = 3/7 and in "vertical" = 1/8

probability of choosing "v" in "reverse" = 1/7 and in "vertical" = 1/8

So, the odds of selecting the SAME letter in both words:

P(R) = 2/7 * 1/8 = 2/56;

P(E) = 3/7 * 1/8 = 3/56;

P(V) = 1/7 * 1/8 = 1/56;

And the odds of making ANY of them is their sum  .

P(the same letter is chosen) = P(same letter is "R") + P(same letter is "E") + P(same letter is "V")

= 6/56 = 3/28 (ANSWER)