Chapter 11.8, Problem 26E

To determine

To explain the probability of at least one coin showing heads when two coins are flipped at the same time.

Explanation of Solution

Given information:

Consider the probability of one coin showing heads is $0.5$ .

Proof:

When two coins are flipped at the same time, the number of possible outcomes are $4$ , $\text{P}\left(\text{heads, heads}\right)$ , $\text{P}\left(\text{heads, tails}\right)$ , $\text{P}\left(\text{tails, heads}\right)$ and $\text{P}\left(\text{tails, tails}\right)$ .

The probability of at least one coin showing heads is $\frac{3}{4}$ or $0.75$ .

Hence, the probability of one coin showing heads is not $0.5+0.5=1.0$