Two dice are thrown simultaneously. What is the probability that the sum of the two numbers appearing on top is a prime number?
Answer and explanation
Correct answer: D. 5/12
- Sum 2: (1,1) [1]
- Sum 3: (1,2), (2,1) [2]
- Sum 5: (1,4), (2,3), (3,2), (4,1) [4]
- Sum 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) [6]
- Sum 11: (5,6), (6,5) [2]
- Sum 3: (1,2), (2,1) [2]
- Sum 5: (1,4), (2,3), (3,2), (4,1) [4]
- Sum 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) [6]
- Sum 11: (5,6), (6,5) [2]
- Step 1: Total outcomes = 6 * 6 = 36.
- Step 2: Prime sums possible between 2 and 12 are: 2, 3, 5, 7, 11.
- Step 3: Total favorable outcomes = 1 + 2 + 4 + 6 + 2 = 15.
- Step 4: Probability = 15 / 36 = 5/12.
Why not the others: Other values result from miscounting the favorable outcomes in the sample space, inverting the probability fraction, or confusing independent with mutually exclusive events.
Practise more Probability.
Free questions with an explanation for every one, and full timed CBSE Class 10 mock tests.
More Probability questions
- A card is drawn at random from a well-shuffled pack of 52 cards. What is the probability of getting a red card?
- A card is drawn at random from a well-shuffled pack of 52 cards. What is the probability of getting a heart?
- A card is drawn at random from a well-shuffled pack of 52 cards. What is the probability of getting an ace?
- A card is drawn at random from a well-shuffled pack of 52 cards. What is the probability of getting a face card?
- A box contains 90 discs numbered from 1 to 90. If one disc is drawn at random from the box, what is the probability that it bears a perfect…
- From a well-shuffled pack of 52 cards, all the kings, queens, and aces are removed. One card is drawn at random from the remaining cards. Wh…