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Question
Find the probability distribution of the number of successes in two tosses of a die, where a success is defined as six appears on at least one die
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Solution
Success is defined as a number six appears on at least one die.
Let X denotes the number of successes.
∴ The possible values of X are 0, 1, 2.
Let P(getting six) = p
= `1/6`
∴ q = 1 – p
= `1 - 1/6`
= `5/6`
∴ P(X = 0) = P(no success)
= q2
= `25/36`
P(X =1) = P(one success)
= pq + qp
= 2pq
= `2 xx 1/6 xx 5/6`
= `10/36`
P(X = 2) = P(two successes)
= pp
= p2
= `1/36`
∴ Probability distribution of X is as follows:
| X | 0 | 1 | 2 |
| P(X = x) | `25/36` | `10/36` | `1/36` |
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