Two fair dice are rolled. The probability that the SUM of the numbers showing is 7 is
A$1/12$
B$1/9$
C$1/6$
D$1/2$
Answer & Solution
Correct answer: C. $1/6$
1. Sample space when rolling 2 dice: $|S| = 6 \times 6 = 36$ equally-likely ordered pairs.
2. Event 'sum = 7': list pairs $(a, b)$ where $a + b = 7$:
$(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)$ → 6 outcomes.
3. $P(\text{sum} = 7) = 6/36 = 1/6$.
4. Interesting: SUM 7 is the most likely sum (more pairs achieve it than any other sum from 2 to 12).
5. Option A gives $3/36$ outcomes (off by half). Option B is $4/36$. Option D would mean 18 outcomes (impossible).
_Source: NCERT Class 11 Mathematics, Ch 14, §14.2.2 + Example 2 (Two-dice events), p. 4 + p. 8._
Related questions
Two coins tossed. P(both heads) =Bag has 4 red, 6 blue. P(red) =Probability of rolling 6 on a die:Probability of heads on a fair coin is:If a fair six-sided die is rolled twice, the probability that the sum is divisible by 3 isA bag has 3 red and 2 black balls. Probability of red ball drawn at random:Probability of getting an even number on rolling a single die:Probability of drawing a king from a standard deck of 52 cards: