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A coin is biased so that the head is 3 times as likely to occur as tail. If the coin is tossed twice, find the probability distribution of number of tails. - Mathematics and Statistics

Question

A coin is biased so that the head is 3 times as likely to occur as tail. If the coin is tossed twice, find the probability distribution of number of tails.

Solution

Given a biased coin such that heads is 3 times as likely as tails.

∴ P(H) = `3/4` and P(T) = `1/4`

The coin is tossed twice.

Let X can be the random variable for the number of tails.

Then X can take the value 0, 1, 2.

∴ P (X = 0) = P (HH) =`3/4 xx 3/4 = 9/16`

P (X = 1) = P (HT, TH) =`3/4 xx 1/4 +1/4 xx 3/4 = 6/16 = 3/8`

P (X = 2) = P (TT) = `1/4 xx 1/4 =1/16`

Therefore, the required probability distribution is as follows.

X 0 1 2
P(X) `9/16` `3/8` `1/16`
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A coin is biased so that the head is 3 times as likely to occur as tail. If the coin is tossed twice, find the probability distribution of number of tails. Concept: Random Variables and Its Probability Distributions.
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