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Two based dice are thrown together. For the first die P(6) = 1/2, the other scores being equally likely while for the second die, P(1) = 2/5 and the other scores are equally likely. Find the probability distribution of the number of ones seen'.

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by Expert (11.2k points)

For first die, P(6) = 1/2 and P(not6) = 1/2
⇒ P(1) + P(2) + P(3) + P(4) + P(5) = 1/2
⇒ P(1) = 1/10 and P(not 1) = 9/10  [∵ P(1) = P(2) = P(3) = P(4) = P(5)]
For second die, P(1) = 2/5 and P(not 1) = 1 - 2/5 = 3/5
Let X =  Number of one's seen
P(X = 0) = P(not 1 on first die). P(not 1 on second die).

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