Question

Kate said to Liam, "If you roll a 5 on a number cube, you win. If I get heads on a coin toss, I win." Is this game fair or unfair? Explain.

Answer 1

A number cube can land on 1, 2, 3, 4, 5, or 6 and all those numbers are equally probable; therefore, the probability of rolling a 5 is

$P(5)=\frac{1}{6}$

On the other hand, when tossing a coin it can only land on heads or tails; thus, the probability of tossing heads is

$P(heads)=\frac{1}{2}$

The two probabilities are not equal; therefore, the game is unfair because is more probable that Kate would win.