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Answer :
Let's consider each question step by step.
Question 1: Probability of Sum of Digits on Dice Being 8 or More
When two dice are thrown, each die can show a number from 1 to 6. The total number of possible outcomes is:
[tex]6 \times 6 = 36.[/tex]
We need to find the probability that the sum of the digits on the dice is 8 or more. Let's list the possible outcomes where the sum is 8 or more:
- Sum of 8: (2,6), (3,5), (4,4), (5,3), (6,2)
- Sum of 9: (3,6), (4,5), (5,4), (6,3)
- Sum of 10: (4,6), (5,5), (6,4)
- Sum of 11: (5,6), (6,5)
- Sum of 12: (6,6)
Counting these outcomes gives us a total of 15 favorable outcomes.
The probability is calculated as:
[tex]\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{15}{36} = \frac{5}{12}.[/tex]
Therefore, the correct option is (B) [tex]\frac{5}{12}[/tex].
Question 2: Probability of a Number Being Divisible by 3 or 7
We have numbers from 1 to 20. We need to find how many of these numbers are divisible by 3 or 7.
- Numbers divisible by 3 within 1 to 20: 3, 6, 9, 12, 15, 18. That's 6 numbers.
- Numbers divisible by 7 within 1 to 20: 7, 14. That's 2 numbers.
To avoid double counting, we check if any number is divisible by both 3 and 7. That would mean divisible by 21, which isn't within the range 1 to 20.
Therefore, the total number of unique favorable outcomes is [tex]6 + 2 = 8[/tex].
The probability is calculated as:
[tex]\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{8}{20} = \frac{2}{5}.[/tex]
However, this option is not among the given choices. Rechecking the problem statement for any discrepancy or error might be necessary. Assuming no error, none of the given options match, indicating a potential mistake in the question part or set of solutions provided.
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