Find the probability distribution of number of number of tails in three tosses of a coin - Mathematics and Statistics

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Sum

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)`
Concept: Probability Distribution of Discrete Random Variables
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Chapter 2.8: Probability Distributions - Q.4

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