#### 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

Let the probability of getting a tail in the biased coin be *x*.

∴ P (T) =* x*

⇒ P (H) = 3*x*

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

When the coin is tossed twice, the sample space is {HH, TT, HT, TH}.

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

Therefore, the required probability distribution is as follows.

X | 0 | 1 | 2 |

P(X) | 9/16 | 3/8 | 1/16 |

Is there an error in this question or solution?

Solution 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.