Question

A number is selected randomly from each of the following two sets:
{1, 2, 3, 4, 5, 6, 7, 8}, {2, 3, 4, 5, 6, 7, 8, 9}
What is the probability that the sum of the numbers is 9?

• A. \(\frac{1}{8}\)
• B. \(\frac{1}{16}\)
• C. \(\frac{3}{32}\)
• D. \(\frac{7}{64}\)

Hint:

Count favorable outcomes by listing all valid pairs. Total outcomes = product of set sizes.

Answer 1

The Correct Option is D

Let \( A = \{1,2,3,4,5,6,7,8\}, B = \{2,3,4,5,6,7,8,9\} \)
Total number of outcomes = \( 8 \times 8 = 64 \)
Now count the number of favorable pairs where \( a + b = 9 \):
From \( A \), possible values: \[ (1,8), (2,7), (3,6), (4,5), (5,4), (6,3), (7,2) \Rightarrow \text{Total = 7 favorable outcomes} \] \[ \text{Required Probability} = \frac{7}{64} \] Final Answer: (4) \(\frac{7}{64}\)