Question

Maria and Isaac are playing a game that involves tossing 5 coins at once. If at least 3 heads are tossed, then Maria wins. If at least 3 tails are tossed, then Isaac wins. Who has a higher probability of winning? Explain."

A) Maria, because she always wins.

B) Isaac, because tails are luckier.

C) Maria, as the probability of getting at least 3 heads is higher.

D) Isaac, as the probability of getting at least 3 tails is higher.

Answer 1

Maria has a higher probability of winning because the probability of getting at least 3 heads is higher.

Step-by-step explanation:

The higher probability of winning in the game between Maria and Isaac can be determined by looking at the probability of getting at least 3 heads or at least 3 tails when tossing 5 coins at once. Based on this information, the probability of getting at least 3 heads is higher than the probability of getting at least 3 tails.

Looking at the 5-coin toss as a whole, there are 10 ways to achieve the macrostate of 3 heads and 2 tails, and there are also 10 ways to achieve the reverse macrostate of 2 heads and 3 tails. In comparison, there is only 1 way to achieve the macrostate of 5 heads or 5 tails. Therefore, the probability of getting at least 3 heads (or tails) is higher than the probability of getting 5 heads (or tails).