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प्रश्न
Three fair coins are tossed simultaneously. If X denotes the number of heads, find the probability distribution of X.
उत्तर
Three fair coins are tossed simultaneously.
∴ S = {HHH , HHT , HTH , THH , HTT , THT , TTH , TTT}
∴ n (S) = 8
X = the number of heads.
∴ Range set of X = {0,1,2,3}
∴ P(X = 0) = P {TTT} = `1/8`
P (X = 1) = P {HTT , THT , TTH} = `3/8`
P (X = 2) = P {HHT , HTH , THH} = `3/8`
P (X = 3) = P {HHH} = `1/8`
Hence the probability distribution of X is as shown in the following table:
| X = x | 0 | 1 | 2 | 3 |
| P (X = x) | `1/8` | `3/8` | `3/8` | `1/8` |
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