Alright, let's solve this step-by-step.
### Step 1: Determine the probability of each die landing on an even number
Each die has 6 faces: 1, 2, 3, 4, 5, 6. Out of these faces, the even numbers are 2, 4, and 6. So, there are 3 even numbers.
The probability of one die landing on an even number is:
[tex]\[ \frac{\text{Number of even faces}}{\text{Total number of faces}} = \frac{3}{6} = 0.5. \][/tex]
### Step 2: Determine the probability of both dice landing on an even number
The result from step 1 tells us that the probability of one die landing on an even number is 0.5.
Now, we need to find the probability of both dice landing on an even number. Since the rolls are independent events, we multiply the probabilities of each die:
[tex]\[ \text{Probability (Both dice even)} = 0.5 \times 0.5 = 0.25. \][/tex]
### Step 3: Predict how many times both dice will land on an even number in 60 rolls
Now that we know the probability of both dice landing on an even number is 0.25, we can use this to find out how many times this event is likely to happen in 60 rolls.
We multiply the probability of the event by the total number of rolls:
[tex]\[ \text{Predicted occurrences} = 60 \times 0.25 = 15. \][/tex]
So, in 60 rolls, we predict that both dice will land on an even number 15 times.
