Question

A six-sided die is biased in such a way that even numbers are three times as likely as odd numbers.what is the probability of observing at least a four on one roll of this die?

Answer 1

Let $P(X=1)=P(X=3)=P(x=5)=a.$

Then $P(X=2)=P(X=4)=P(x=6)=3a.$

$$a+3a+a+3a+a+3a=1$$

$$a=\dfrac{1}{12}$$

Hence

$$P(X=4)=3(\dfrac{1}{12})=\dfrac{1}{4}$$