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Question
Find the probability distribution of number of tails in the simultaneous tosses of three coins.
Solution
When three coins are tossed simultaneously, the sample space is
{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
Let X represent the number of tails.
It can be seen that X can take the value of 0, 1, 2 or 3
P(X = 0) = P(HHH) = `1/8`
P(X = 1) = P(HHT) + P(HTH) + P(THH) =`1/8 +1/8+1/8 =3/8`
P(X = 2) = P(HTT) + P(THT) + P(TTH) =`1/8+1/8+1/8 = 3/8`
P(X = 3) = P(TTT) = `1/8`
Thus, the probability distribution is as follows.
| X | 0 | 1 | 2 | 3 |
| P(X) | `1/8` | `3/8` | `3/8` | `1/8` |
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