Question

The table shows the possible outcomes of spinning a fair spinner twice with sections labeled A, B, C, and D.

A B C D
A A, A A, B A, C A, D
B B, A B, B B, C B, D
C C, A C, B C, C C, D
D D, A D, B D, C D, D
If you repeat this experiment 360 times, how many repetitions do you predict will result in the same letter being spun for both spins?

Answer 1

We predict that 90 repetitions out of 360 will result in the same letter being spun for both spins.

Explanation:

To determine the number of repetitions that will result in the same letter being spun for both spins, we can analyze the table provided.

From the table, we can see that there are 4 possible outcomes where the same letter is spun in both spins: (A, A), (B, B), (C, C), and (D, D). Each of these outcomes has a probability of 1/4 since the spinner is fair.

If the experiment is repeated 360 times, the expected number of repetitions resulting in the same letter being spun in both spins can be calculated by multiplying the probability of each outcome by the total number of repetitions.

Expected number of repetitions = (1/4) * 360 = 90

Answer 2

There are 25 possible outcomes for spinning a fair spinner twice. There are 5 outcomes that result in the same letter being spun for both spins: AA, BB, CC, DD, and AA. Therefore, we would expect 5/25 = 20% of the repetitions to result in the same letter being spun for both spins. If we repeat the experiment 360 times, we would predict that 360 * 0.2 = 72 repetitions will result in the same letter being spun for both spins.

Here is a more detailed explanation of how we arrived at this answer:

* There are 25 possible outcomes for spinning a fair spinner twice. This is because there are 5 possible letters that can be spun on each spin, and there are 5 * 5 = 25 possible combinations of letters.

* There are 5 outcomes that result in the same letter being spun for both spins. This is because there is one outcome for each of the 5 possible letters.

* Therefore, we would expect 5/25 = 20% of the repetitions to result in the same letter being spun for both spins. This is because there are 5 outcomes that result in the same letter being spun for both spins, and there are a total of 25 possible outcomes.

* If we repeat the experiment 360 times, we would predict that 360 * 0.2 = 72 repetitions will result in the same letter being spun for both spins. This is because there is a 20% chance of the same letter being spun for both spins on each repetition, and we are repeating the experiment 360 times.

Explanation: