Question:
Two dice are thrown at the same time. What is the probability that the sum of the two numbers appearing on the top of the dice is more than 10?
Two dice are thrown at the same time. What is the probability that the sum of the two numbers appearing on the top of the dice is more than 10?
Updated On: Apr 29, 2025
- \(\frac {1}{36}\)
- \(\frac {1}{12}\)
- \(\frac {1}{26}\)
- \(\frac {1}{13}\)
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
When two dice are thrown, there are a total of $6 \times 6 = 36$ possible outcomes.
We want to find the number of outcomes where the sum of the two numbers is more than 10.
This means the sum is 11 or 12.
The outcomes that result in a sum of 11 are: (5, 6) and (6, 5)
The outcomes that result in a sum of 12 are: (6, 6) So, there are 2 outcomes with a sum of 11 and 1 outcome with a sum of 12. The total number of outcomes where the sum is more than 10 is $2 + 1 = 3$.
Therefore, the probability that the sum of the two numbers is more than 10 is: $$ P(\text{sum} > 10) = \frac{\text{Number of outcomes with sum > 10}}{\text{Total number of outcomes}} = \frac{3}{36} = \frac{1}{12} $$ The probability is $\frac{1}{12}$.
Was this answer helpful?
5
1
Top Questions on Probability
- Find the probability distribution of the number of boys in families having three children, assuming equal probability for a boy and a girl.
- If $P(A) = \frac{1}{7}$, $P(B) = \frac{5}{7}$ and $P(A \cap B) = \frac{4}{7}$, then $P(A | B)$ is:
- If $ A $ and $ B $ are two events such that $ P(A) = 0.7 $, $ P(B) = 0.4 $ and $ P\left( A \cap \overline{B} \right) = 0.5 $, where $\overline{B}$ denotes the complement of $ B $, then $ P\left( B | \left( A \cup \overline{B} \right) \right) $ is equal to
- JEE Main - 2025
- Mathematics
- Probability
- If the probability that the random variable X takes the value x is given by \( P(X = x) = k(x + 1)3^{-x} \), \( x = 0, 1, 2, 3, ... \), where k is a constant, then \( P(X \ge 3) \) is equal to
- JEE Main - 2025
- Mathematics
- Probability
- All five letter words are made using all the letters A, B, C, D, E and arranged as in an English dictionary with serial numbers. Let the word at serial number $ n $ be denoted by $ W_n $. Let the probability $ P(W_n) $ of choosing the word $ W_n $ satisfy $ P(W_n) = 2P(W_{n-1}) $, $ n>1 $. If $ P(CDBEA) = \frac{2^\alpha}{2^\beta - 1} $, $ \alpha, \beta \in \mathbb{N} $, then $ \alpha + \beta $ is equal to :
- JEE Main - 2025
- Mathematics
- Probability
View More Questions
Questions Asked in AP POLYCET exam
- The points \( (1,5), (2,3) \) and \( (-2, -11) \) form a:
- Which of the following is not irrational?
- AP POLYCET - 2025
- Rational or Irrational Numbers
- If assumed mean of a data is 47.5, \( \sum f_i d_i = 435 \) and \( \sum f_i = 30 \), then mean of that data is:
- AP POLYCET - 2025
- Arithmetic Mean
- The solution of \( x - 2y = 0 \) and \( 3x + 4y - 20 = 0 \) is:
- AP POLYCET - 2025
- Linear Equations
- A prime number \( p \) divides \( a^2 \) where \( a \) is a positive integer, then
- AP POLYCET - 2025
- Prime and Composite Numbers
View More Questions