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Question
Solve the following problem :
Find the probability of the number of successes in two tosses of a die, where success is defined as number greater than 4.
Solution
Success is defined as a number greater than 4 appears on at least one die.
Let X denote the number of successes.
∴ Possible values of X and 0, 1, 2.
Let, P(getting a number greater than 4) = p = `(2)/(6) = (1)/(3)`
∴ q = 1 – p = `1 - (1)/(3) = (2)/(3)`
∴ P(X = 0) = P(no success) = qq = q2 = `(4)/(9)`
9 P(X = 1) = P(one success) = qp + qp = 2pq
= `(2 xx 1)/(3) xx (2)/(3)`
= `(4)/(9)`
P(X = 2) = P(two successes) = pp = p2 = `(1)/(9)`
∴ Probability distribution of X is as follows:
| X | 0 | 1 | 2 |
| P(X = x) | `(4)/(9)` | `(4)/(9)` | `(1)/(9)` |
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