An unbiased six-faced dice whose faces are marked with numbers 1, 2, 3, 4, 5,
and 6 is rolled twice in succession and the number on the top face is recorded
each time. The probability that the sum of the two recorded numbers is a prime
number is ________
An unbiased six-faced dice whose faces are marked with numbers 1, 2, 3, 4, 5,
and 6 is rolled twice in succession and the number on the top face is recorded
each time. The probability that the sum of the two recorded numbers is a prime
number is ________
Show Hint
- 3 36
- 13 36
- 15 36
- 19 36
The Correct Option is C
Solution and Explanation
Step 1: When two dice are rolled, the total number of equally likely outcomes is \(6 \times 6 = 36\).
Step 2: The possible sums range from 2 to 12. Among these, the prime sums are \(2, 3, 5, 7, 11\) (note that 9 is not prime).
Step 3: Count the ordered pairs (first die, second die) giving each prime sum: Sum = 2: (1,1) -- 1 way. Sum = 3: (1,2),(2,1) -- 2 ways. Sum = 5: (1,4),(4,1),(2,3),(3,2) -- 4 ways. Sum = 7: (1,6),(6,1),(2,5),(5,2),(3,4),(4,3) -- 6 ways. Sum = 11: (5,6),(6,5) -- 2 ways.
Step 4: Total favourable outcomes = \(1 + 2 + 4 + 6 + 2 = 15\).
Step 5: Probability = \(\dfrac{15}{36}\).
Final Answer: \(\boxed{\dfrac{15}{36}}\) (option C)
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