Question

A coin is biased so that heads is three times as likely to appear as tails. Find $P\left(H\right)$ and $P\left(T\right)$. If such a coin is tossed twice find the probability that head occurs at least once.

Answer 1

Given that heads is $3$ times as likely as tails.

Coin tossed twice.

$P\left(H\right)=3_{/4}$, $P\left(T\right)=1_{/4}$

gives heads atleast once

$P\left(HH\right)=\frac{3}{4}\times \frac{3}{4}=\frac{9}{16}$

$P(HT,TH)=\frac{3}{4}\times \frac{1}{4}+\frac{3}{4}\times \frac{1}{4}=\frac{3}{8}$.