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.

Given: head is 3 times as likely to occur as tail.

Now, let the probability of getting a tail in the biased coin be x.

⇒ P(T) = x

And P(H) = 3x

For a biased coin, P(T) + P(H) = 1

⇒ x + 3x = 1

⇒ 4x = 1

⇒ x = 1/4

Hence, P(T) = 1/4 and P(H) = 3/4

As the coin is tossed twice, so the sample space is {HH, HT, TH, TT}

Let X be a random variable representing the number of tails.

Clearly, X can take the value of 0, 1 or 2.

P(X = 0) = P(no tail) = P(H) × P(H)

P(X = 1) = P(one tail) = P(HT) × P(TH)

P(X = 2) = P(two tail) = P(T) × P(T)

Hence, the required probability distribution is,

X | 0 | 1 | 2 |

P(X) |

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