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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 = x) | `9/16` | `3/8` | `1/16` |
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