Single correct option
Two fair six-sided dice are rolled. Given that at least one die shows a 3, what is the probability that the sum of the two numbers is a prime number?
- A. 4/11
- B. 5/11
- C. 1/3
- D. 2/11
Show answer and solution
Answer: (A) 4/11
Outcomes with at least one 3: 6 + 6 − 1 = 11 (the (3, 3) case counted once).
Sums: (3,1)=4, (3,2)=5, (3,3)=6, (3,4)=7, (3,5)=8, (3,6)=9, and (1,3)=4, (2,3)=5, (4,3)=7, (5,3)=8, (6,3)=9.
Prime sums: (3,2), (2,3), (3,4), (4,3) → 4 outcomes.
P = 4/11.
The trap 1/3 comes from using 12 outcomes (double counting (3, 3)).
Sums: (3,1)=4, (3,2)=5, (3,3)=6, (3,4)=7, (3,5)=8, (3,6)=9, and (1,3)=4, (2,3)=5, (4,3)=7, (5,3)=8, (6,3)=9.
Prime sums: (3,2), (2,3), (3,4), (4,3) → 4 outcomes.
P = 4/11.
The trap 1/3 comes from using 12 outcomes (double counting (3, 3)).
Saved on this device. Sign in or create a free account to keep it on every device.