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Find the probability distribution of number of number of tails in three tosses of a coin

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#### Solution

Let X denote the number of tails.

Sample space of the experiment is

S = {HHH, HHT, HTH, THH, TTT, TTH, THT, HTT}

The values of X corresponding to these outcomes are as follows.

X(HHH) = 0

X(HHT) = X(HTH) = X(THH) = 1

X(TTH) = X(THT) = X(HTT) = 2

X(TTT) = 3

∴ X is a discrete random variable that can take values 0, 1, 2, 3.

**The probability distribution of X is then obtained as follows:**

X |
0 | 1 | 2 | 3 |

P(X = x) |
`(1)/(8)` | `(3)/(8)` | `(3)/(8)` | `(1)/(8)` |

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