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प्रश्न
Solve the following problem :
Find the probability of the number of successes in two tosses of a die, where success is defined as six appears in at least one toss.
उत्तर
Success is defined as a number six appears on at least one die.
Let X denote the number of successes.
∴ 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) = qq = 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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