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प्रश्न
Find the probability distribution of the number of heads, when three coins are tossed.
उत्तर
Let X denote the number of heads in three tosses of a coin. Then, X can take the values 0, 1, 2 and 3.
Now,
\[P\left( X = 0 \right) = P\left(\text{ TTT }\right) = \frac{1}{8}, P\left( X = 1 \right) = P\left(\text{HTT or TTH or THT }\right) = \frac{3}{8}\]
\[P\left( X = 2 \right) = P\left(\text{ HTH or THH or HHT }\right) = \frac{3}{8}, P\left( X = 3 \right) = P\left( HHH \right) = \frac{1}{8}\]
Thus, the probability distribution of X is given by
| x | P (X) |
| 0 |
\[\frac{1}{8}\]
|
| 1 |
\[\frac{3}{8}\]
|
| 2 |
\[\frac{3}{8}\]
|
| 3 |
\[\frac{1}{8}\]
|
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