Solution
Long Answer
When a dice is rolled once, probability of obtaining six =
and probability of obtaining a non-six =
P(X = 2) = P(six on both the dice) =
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Two die are thrown simultaneously. If X denote the number sixes, find the expectation of X.
Solution
Let X be the random variable which denotes the number of sixes on two dice. So, X may have values 0,1 or 2.
When a dice is rolled once, probability of obtaining six =16 and probability of obtaining a non-six =55
P(X =0) =P (non-six on both dice)=56×56=2536
P(X=1)=P (six on first and non -six on the second)+P(non-six on the first and six on the second)
=16×56+16×56=1036
P(X=2)=P(six on both the dice) =16×16=136
Therefore, the required probability distribution is as follows:
X 0 1 2P(X)25361036136
∴ Expectation of X=mean of the variable X
=∑X P(X)=0×2536+1×1036×+2×136=1236=13.
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