The mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on one face is

1

2

5

$8 over 3$

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Solution

Let X denote the number on the die, then X takes values 1, 2 and 5 only.
P(X = 1) =

3 over 6 space equals space 1 half comma space space space space straight P left parenthesis straight X space equals space 2 right parenthesis space equals 2 over 6 space equals 1 third comma space space straight P left parenthesis straight X space equals space 5 right parenthesis space equals space 1 over 6

∴ probability distribution of X is

Mean space straight X space equals space sum from blank to blank of straight X space straight P left parenthesis straight X right parenthesis space equals space 1 space cross times 1 half plus 2 cross times 1 third plus 5 space cross times 1 over 6 space equals space 1 half plus 2 over 3 plus 5 over 6 space equals fraction numerator 3 plus 4 plus 5 over denominator 6 end fraction space equals 12 over 6 space equals 2

∴ (B) is correct answer.

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