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Question
Three fair coins are tossed simultaneously. Find the probability mass function for a number of heads that occurred
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Solution
When three coins are tossed, the sample space is
S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
‘X’ is the random variable that denotes the number of heads.
∴ ‘X’ can take the values of 0, 1, 2 and 3
Sample space S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}
| Values of random variable | 0 | 1 | 2 | 3 | Total |
| Number of elements in inverse image | 1 | 3 | 3 | 1 | 8 |
Probability mass function
| x | 0 | 1 | 2 | 3 |
| f(x) = P(X = x) | `1/8` | `3/8` | `3/8` | `1/8` |
or
f(x) = `{{:(1/8, "for" x = 0",", 3),(3/8, "for" x = 1",", 2):}`
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