Two dice are thrown then the probability of the sum of numbers appearing to be prime is :
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( \displaystyle\frac{15}{36} \)
Two dice give 36 equally likely outcomes, with sums from 2 to 12. The prime sums are 2, 3, 5, 7 and 11:
sum 2: (1, 1), 1 way
sum 3: (1, 2), (2, 1), 2 ways
sum 5: (1, 4), (2, 3), (3, 2), (4, 1), 4 ways
sum 7: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1), 6 ways
sum 11: (5, 6), (6, 5), 2 ways
\( \displaystyle P=\frac{1+2+4+6+2}{36} \)
\( \displaystyle =\frac{15}{36} \)