A children's game has a spinner that is equally likely to land on any 1 of 4 colors: red, blue, yellow, or green. Determine the probability of spinning a red both times on 2 spins. Explain your reasoning.

To determine the probability of spinning a red both times on two spins, we need to consider the total number of possible outcomes and the number of favorable outcomes.

First, let's determine the total number of possible outcomes. Since the spinner has an equal chance of landing on any of the 4 colors (red, blue, yellow, or green), there are 4 equally likely outcomes for each spin. Thus, the total number of possible outcomes for the two spins can be found by multiplying the number of outcomes for each spin. So, the total number of possible outcomes is 4 x 4 = 16.

Next, let's determine the number of favorable outcomes, which in this case is spinning a red both times. Since the spinner has an equal chance of landing on any of the 4 colors, the probability of spinning a red on the first spin is 1/4. Similarly, the probability of spinning a red on the second spin is also 1/4 because each spin is independent of the other. To find the probability of both events occurring, we multiply these probabilities together. So, the number of favorable outcomes is (1/4) x (1/4) = 1/16.

Finally, we can determine the probability of spinning a red both times by dividing the number of favorable outcomes by the total number of possible outcomes. In this case, the probability is (1/16) / (16/16) = 1/16.

Therefore, the probability of spinning a red both times on two spins is 1/16, or 0.0625, which is approximately 6.25%.