The problem asks how many times Wiley can expect to get an outcome of tails and an odd number when flipping a fair coin and rolling a fair die, over 480 trials.

Step 1: Identify favorable outcomes

The possible outcomes when flipping a coin are Heads (H) and Tails (T), and the possible outcomes when rolling a die are the numbers 1 through 6.

• Wiley is interested in the outcome Tails (T) and an odd number.
• The odd numbers on the die are 1, 3, and 5.

From the table, the favorable outcomes are:

• T, 1
• T, 3
• T, 5

There are 3 favorable outcomes.

Step 2: Calculate the probability

There are 12 possible outcomes in total (2 outcomes from the coin × 6 outcomes from the die).

The probability of getting Tails and an odd number is: $\frac{3 \text{ favorable outcomes}}{12 \text{ total outcomes}} = \frac{1}{4}$

Step 3: Use the probability to find the expected value

Wiley repeats the experiment 480 times. The expected number of favorable outcomes is: $\text{Expected outcomes} = \text{Probability} \times \text{Total trials} = \frac{1}{4} \times 480 = 120$

Final Answer:

Wiley can expect to get an outcome of tails and an odd number 120 times.

Would you like more details or have any questions?

Here are some related questions you might find interesting:

1. What is the probability of getting heads and an even number?
2. If Wiley performs the experiment 600 times, how many tails and odd numbers are expected?
3. What if Wiley used a die with 8 faces, how would the probabilities change?
4. How would the result change if the coin was biased and came up heads 70% of the time?
5. What is the total probability of getting any tails, regardless of the die outcome?

Tip: When calculating probabilities in combined events, remember to multiply the individual probabilities of each independent event (like flipping a coin and rolling a die).