Question:
Two unbiased dice are thrown. Then the probability that neither a doublet nor a total of 10 will appear is
Two unbiased dice are thrown. Then the probability that neither a doublet nor a total of 10 will appear is
Show Hint
Using the complement rule $P(\text{Neither A nor B}) = 1 - P(A \cup B)$ is the most efficient way to solve "neither/nor" probability questions.
Updated On: Jun 4, 2026
- $\frac{1}{12}$
- $\frac{1}{36}$
- $\frac{2}{9}$
- $\frac{7}{9}$
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: Understanding the Question:
We need to calculate the probability of not getting a doublet and not getting a sum of 10 when rolling two dice.
Step 2: Key Formula or Approach:
Find the total number of outcomes. Find the number of outcomes for getting a doublet and getting a sum of 10. Subtract the union of these outcomes from the total to find the favorable outcomes, then divide by the total.
Step 3: Detailed Explanation:
Total possible outcomes when two dice are thrown $= 6 \times 6 = 36$.
Let $A$ be the event of getting a doublet: $A = \{(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)\}$. There are 6 ways.
Let $B$ be the event of getting a total of 10: $B = \{(4,6), (5,5), (6,4)\}$. There are 3 ways.
The intersection $A \cap B$ (getting a doublet and a total of 10) is $\{(5,5)\}$, which is 1 way.
Using the principle of inclusion-exclusion, the total number of ways to get a doublet or a total of 10 is:
$$n(A \cup B) = n(A) + n(B) - n(A \cap B) = 6 + 3 - 1 = 8$$ The number of favorable outcomes (neither a doublet nor a total of 10) is $36 - 8 = 28$.
Required probability $= \frac{28}{36} = \frac{7}{9}$.
Step 4: Final Answer:
The required probability is $\frac{7}{9}$, matching option (D).
We need to calculate the probability of not getting a doublet and not getting a sum of 10 when rolling two dice.
Step 2: Key Formula or Approach:
Find the total number of outcomes. Find the number of outcomes for getting a doublet and getting a sum of 10. Subtract the union of these outcomes from the total to find the favorable outcomes, then divide by the total.
Step 3: Detailed Explanation:
Total possible outcomes when two dice are thrown $= 6 \times 6 = 36$.
Let $A$ be the event of getting a doublet: $A = \{(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)\}$. There are 6 ways.
Let $B$ be the event of getting a total of 10: $B = \{(4,6), (5,5), (6,4)\}$. There are 3 ways.
The intersection $A \cap B$ (getting a doublet and a total of 10) is $\{(5,5)\}$, which is 1 way.
Using the principle of inclusion-exclusion, the total number of ways to get a doublet or a total of 10 is:
$$n(A \cup B) = n(A) + n(B) - n(A \cap B) = 6 + 3 - 1 = 8$$ The number of favorable outcomes (neither a doublet nor a total of 10) is $36 - 8 = 28$.
Required probability $= \frac{28}{36} = \frac{7}{9}$.
Step 4: Final Answer:
The required probability is $\frac{7}{9}$, matching option (D).
Was this answer helpful?
0
0
Top MHT CET Mathematics Questions
- The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is
- If $\int\frac{f\left(x\right)}{log \left(sin\,x\right)}dx = log\left[log\,sin\,x\right]+c$ then $f\left(x\right)=$
- If $\int\limits^{K}_0 \frac{dx}{2 + 18 x^2} = \frac{\pi}{24}$, then the value of K is
- If $\int^{\pi/2}_{0} \log\cos x dx =\frac{\pi}{2} \log\left(\frac{1}{2}\right)$ then $ \int^{\pi/2}_{0} \log\sec x dx = $
- The point on the curve $y = \sqrt{x - 1}$ where the tangent is perpendicular to the line $2x + y - 5 = 0 $ is
View More Questions
Top MHT CET Probability Questions
- If $r. v. x :$ waiting time in minutes for bus and $p.d.f.$ of $x$ is given by $f(x) = \begin{cases} \frac{1}{5} , & 0\le x\le5 \\[2ex] 0, & \text{otherwise} \end{cases}$ then probability of waiting time not more than $4$ minutes is = _______
- A die is thrown twice. If getting a number greater than four on the die is considered a success, then the variance of the probability distribution of the number of successes is
- If $r.v. X \sim B \left(n = 5, P=\frac{1}{3}\right)$ then $P(2 < X < 4) =$ ______________
- Given $ P(A \cup B ) = 0.6,P(A\cap B) = 0.2 $ , the probability of exactly one of the event occurs is
- From a group of $ 8 $ boys and $ 3 $ girls, a commitee of $ 5 $ members to be formed. Find the probability that $ 2 $ particular girls are included in the committe is
View More Questions
Top MHT CET Questions
- During r- DNA technology, which one of the following enzymes is used for cleaving DNA molecule ?
- In non uniform circular motion, the ratio of tangential to radial acceleration is (r = radius of circle, $v =$ speed of the particle, $\alpha =$ angular acceleration)
- The temperature of $32^{\circ}C$ is equivalent to
- The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is
- The heat of formation of water is $ 260\, kJ $ . How much $ H_2O $ is decomposed by $ 130\, kJ $ of heat ?
View More Questions