1.

A fair die is thrown once. A person will get Rs. 5 if the die results in multiplying 3. Otherwise he loses Rs 2. Find his expectations.

Answer»

Let X denote expected amount, which takes the values X : 5 and - 2. With respective probabilities as:

P(x = 5) = P(getting muItiple of 3)

= 2/6 ; {i.e. 3,6}

P(x = 2) = 4/6; {i. e.1,2,4,5}

The probability of distribution is

X5-2
p(X)2/64/6

Expected amount: E(X) = ΣX.P(X)

= 5 x 2/6 -2 x 4/6 = 1 - 67 - 1.33 

= 0.34 i.e. 34 paise gain.



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