A fair coin is flipped four times. Use a tree diagram to find the probability of observing exactly two heads. Enter your answer as a percentage, to the nearest percent.

We are asked to find the probability of obtaining exactly two heads when a fair coin is flipped four times. 1. **Total Outcomes:** Each coin flip has 2 possibilities, so for 4 flips, the total number of outcomes is \[ 2^4 = 16. \] 2. **Tree Diagram Approach:** A tree diagram would start at a root and branch out at each coin flip. For example, the first flip branches into \(H\) (head) and \(T\) (tail). Each of these branches again splits into \(H\) and \(T\) for the second flip, and similarly for the third and fourth flips. Although drawing the full tree diagram on paper is helpful to visualize all \(16\) outcomes, each branch represents a possible sequence of heads and tails. 3. **Counting Favorable Outcomes:** We want the outcome to have exactly 2 heads. The number of ways to choose 2 flips out of 4 to be heads is given by the combination \[ \binom{4}{2}. \] Calculating this gives: \[ \binom{4}{2} = \frac{4!}{2! \cdot 2!} = \frac{24}{4} = 6. \] 4. **Calculating the Probability:** The probability of exactly 2 heads is the number of favorable outcomes divided by the total number of outcomes: \[ \text{Probability} = \frac{6}{16} = 0.375. \] 5. **Expressing as a Percentage:** Converting \(0.375\) to a percentage: \[ 0.375 \times 100\% = 37.5\% \] Rounding to the nearest percent gives approximately \(38\%\). Thus, the probability of observing exactly two heads is approximately \(38\%\).