To determine which event is least likely to occur when rolling two six-sided number cubes (with outcomes 1 through 6), let's analyze each option:
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The two number cubes add up to an even number.
- A sum is even if both numbers are even or both are odd. Each cube has 3 even numbers (2, 4, 6) and 3 odd numbers (1, 3, 5).
- The combinations that yield an even sum can be calculated as follows:
- Both even: \(3 \times 3 = 9\) combinations
- Both odd: \(3 \times 3 = 9\) combinations
- Total combinations for an even sum: \(9 + 9 = 18\).
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Both number cubes land on an odd number.
- There are 3 odd numbers (1, 3, 5).
- The combinations for both cubes landing on odd numbers: \(3 \times 3 = 9\).
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One number cube lands on an even number, and one number cube lands on 3.
- One cube is even (2, 4, or 6) and the other is 3.
- The combinations are:
- Even on the first cube and 3 on the second: \(3 \times 1 = 3\)
- 3 on the first cube and even on the second: \(1 \times 3 = 3\)
- Total combinations: \(3 + 3 = 6\).
-
One number cube lands on 6, and the other lands on 3.
- There are exactly two combinations: (6, 3) or (3, 6).
- Total combinations: \(2\).
Now we can summarize the likelihood of each event:
- Even sum: 18 combinations
- Both odd: 9 combinations
- One even and one 3: 6 combinations
- One 6 and one 3: 2 combinations
Thus, the least likely event to occur is:
One number cube lands on 6, and the other lands on 3.