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Three fair coins are tossed simultaneously. Find the probability mass function for number of heads occurred. |
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Answer» When three coins are tossed, the sample space is S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT} ‘X’ is the random variable denotes the number of heads. ∴ ‘X’ can take the values of 0, 1, 2 and 3 Hence, the probabilities P(X = 0) = P (No heads) = 1/8; P(X = 1) = P (1 head) = 3/8; P(X = 2) = P (2 heads) = 3/8; P(X = 3) = P (3 heads)=1/8; ∴ The probability mass function is f(x) = \(\begin{cases} 1/8&for&x=0,3\\3/8&for &x=1,2\end{cases}\) |
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