A number is chosen from each of the two sets {1 , 2 , 3, 4, 5, 6 , 7. 8 , 9} and {1, 2 . 3, 4, 5, 6 , 7, 8 , 9}. If p1denotes the probability that the sum of the two numbers be 10 and p2the probability that their sum be 8, then (p1 + p2] isa)7/729b)137/729c)16/81d)137/81Correct answer is option 'C'. Can you explain this answer?

Question

Answer

To find the probability of the sum of two numbers being 10 or 8, we need to find the total number of favorable outcomes and divide it by the total number of possible outcomes.

Step 1: Counting the favorable outcomes for the sum of 10.
To get a sum of 10, the first number can be any number from the first set, and the second number will be the difference between 10 and the first number.

- If the first number is 1, the second number will be 9.
- If the first number is 2, the second number will be 8.
- If the first number is 3, the second number will be 7.
- If the first number is 4, the second number will be 6.
- If the first number is 5, the second number will be 5.
- If the first number is 6, the second number will be 4.
- If the first number is 7, the second number will be 3.
- If the first number is 8, the second number will be 2.
- If the first number is 9, the second number will be 1.

So, there are a total of 9 favorable outcomes for the sum of 10.

Step 2: Counting the favorable outcomes for the sum of 8.
To get a sum of 8, the first number can be any number from the first set, and the second number will be the difference between 8 and the first number.

- If the first number is 1, the second number will be 7.
- If the first number is 2, the second number will be 6.
- If the first number is 3, the second number will be 5.
- If the first number is 4, the second number will be 4.
- If the first number is 5, the second number will be 3.
- If the first number is 6, the second number will be 2.
- If the first number is 7, the second number will be 1.
- If the first number is 8, the second number will be 0. (But 0 is not in the second set)

So, there are a total of 7 favorable outcomes for the sum of 8.

Step 3: Counting the total number of outcomes.
Each number from the first set can be paired with any number from the second set, so the total number of outcomes is 9 * 9 = 81.

Step 4: Calculating the probabilities.
The probability of the sum being 10 is the number of favorable outcomes (9) divided by the total number of outcomes (81), which is 9/81 = 1/9.

The probability of the sum being 8 is the number of favorable outcomes (7) divided by the total number of outcomes (81), which is 7/81.

Therefore, the required probability (p1 + p2) is (1/9 + 7/81) = 16/81.

Hence, the correct answer is option C) 16/81.

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