COMEDK2024Morning ShiftMathematicsProbabilityActual
A and B each have a calculator which can generate a single digit random number from the set 1,2,3,4,5,6,7,8 . They can generate a random number on their calculator. Given that the sum of the two numbers is 12 , then the probability that the two numbers are equal is
Options
- A1 8
- B5 64
- C1 5
- D1 16
Correct answer
C. 1 5
Step-by-step solution
Let X be the number generated by A and Y be the number generated by B, where X, Y 1, 2, 3, 4, 5, 6, 7, 8 . The total number of possible outcomes is 8 8 = 64 . We are given that the sum X + Y = 12 . The possible pairs (X, Y) that satisfy this condition are: (4, 8), (5, 7), (6, 6), (7, 5), (8, 4) . The number of favorable outcomes where the sum is 12 is 5. Let S be the event that X + Y = 12 . Then n(S) = 5 . We want to find the probability that the two numbers are equal, given that their sum is 12. Let E be the event