Valerie plays a game using the spinner shown. During the game she will spin a total of 36 times.

Which is the best prediction for the number of times she will get either "lose a turn" or "back 3" on the spinner?

To find the best prediction for the number of times Valerie will get either "lose a turn" or "back 3" on the spinner, we need to look at the probabilities associated with those outcomes.

Let's first determine the probability of getting "lose a turn." From the spinner, we can see that there are 4 equally likely outcomes (4 sections with "lose a turn" on them) out of a total of 12 sections. Therefore, the probability of getting "lose a turn" on each spin is 4/12, which simplifies to 1/3.

Next, we can determine the probability of getting "back 3." Again, there are 4 sections with "back 3" on them out of a total of 12 sections, so the probability of getting "back 3" on each spin is also 4/12 or 1/3.

Since each spin is independent of the others, we can multiply the probability of each outcome by the total number of spins (36) to find the expected number of times we would expect to get each outcome:

Expected number of "lose a turn" = (1/3) * 36 = 12
Expected number of "back 3" = (1/3) * 36 = 12

Therefore, the best prediction for the number of times Valerie will get either "lose a turn" or "back 3" on the spinner is 12 times.