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प्रश्न
Find the probability distribution of number of heads in two tosses of a coin.
If two coins are tossed simultaneously, write the probability distribution of the number of heads.
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उत्तर
When one coin is tossed twice, the sample space is
{HH, HT, TH, TT}
Let X represent the number of heads s in two tosses of a coin.
∴ X(HH) = 2,
X(HT) = 1,
X(TH) = 1,
X(TT) = 0
Therefore, X can take the value of 0, 1 or 2.
It is known that,
P(HH) = P(HT) = P(TH) = P(TT) = `1/4`
P(X = 0) = P(TT) = `1/4`
P(X = 1) = P(HT) + P(TH) = `1/4 +1/4 = 1/2`
P(X = 2) = P(HH) = `1/4`
Thus, the required probability distribution is as follows:
| X | 0 | 1 | 2 |
| P(X) | `1/4` | `1/2` | `1/4` |
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