Question:
Consider a case where two identical six-faced fair dice are rolled simultaneously.
The probability of getting even numbers in both AND a sum equal to 5 and above is ______ (rounded off to two decimal places).
Consider a case where two identical six-faced fair dice are rolled simultaneously.
The probability of getting even numbers in both AND a sum equal to 5 and above is ______ (rounded off to two decimal places).
The probability of getting even numbers in both AND a sum equal to 5 and above is ______ (rounded off to two decimal places).
Show Hint
First list the outcomes where both dice are even, then keep only those with sum 5 or more.
Updated On: Jul 28, 2026
Show Solution
Verified By Collegedunia
Correct Answer: 0.22
Solution and Explanation
Step 1: List the sample space.
Two dice give \(6 \times 6 = 36\) equally likely outcomes.
We need outcomes where both numbers are even AND their sum is 5 or more.
Step 2: List the even-even outcomes.
Each die shows 2, 4 or 6, giving \(3 \times 3 = 9\) outcomes: (2,2), (2,4), (2,6), (4,2), (4,4), (4,6), (6,2), (6,4), (6,6).
Step 3: Apply the sum condition.
The pair (2,2) sums to 4, which fails the "sum 5 and above" condition.
All the other 8 pairs, (2,4)=6, (2,6)=8, (4,2)=6, (4,4)=8, (4,6)=10, (6,2)=8, (6,4)=10, (6,6)=12, satisfy sum \(\ge 5\).
So 8 out of the 36 total outcomes meet both conditions.
Final Answer:
The probability is \(\dfrac{8}{36} = 0.2\overline{2}\), rounded to 0.22.
\[ \boxed{0.22} \]
Two dice give \(6 \times 6 = 36\) equally likely outcomes.
We need outcomes where both numbers are even AND their sum is 5 or more.
Step 2: List the even-even outcomes.
Each die shows 2, 4 or 6, giving \(3 \times 3 = 9\) outcomes: (2,2), (2,4), (2,6), (4,2), (4,4), (4,6), (6,2), (6,4), (6,6).
Step 3: Apply the sum condition.
The pair (2,2) sums to 4, which fails the "sum 5 and above" condition.
All the other 8 pairs, (2,4)=6, (2,6)=8, (4,2)=6, (4,4)=8, (4,6)=10, (6,2)=8, (6,4)=10, (6,6)=12, satisfy sum \(\ge 5\).
So 8 out of the 36 total outcomes meet both conditions.
Final Answer:
The probability is \(\dfrac{8}{36} = 0.2\overline{2}\), rounded to 0.22.
\[ \boxed{0.22} \]
Was this answer helpful?
0
0
Top GATE NM Engineering Mathematics Questions
- The determinant of the matrix \( \begin{pmatrix} 1 & p & q+r \\ 1 & q & r+p \\ 1 & r & p+q \end{pmatrix} \) is ______.
- The gradient of a scalar field is ______.
- Which ONE of the following curves represents the equation \( y = e^{-x} \)?
Figures not to scale - The Fourier series expansion of the function \( f(x) = |\cos(x)| \) in the interval \( (-\pi, \pi) \) is \( \alpha + \beta \left[ \dfrac{1}{3}\cos(2x) - \dfrac{1}{15}\cos(4x) + \cdots \right] \).
The values of \( \alpha \) and \( \beta \) respectively are ______. - Which of the following ordinary differential equations is/are linear?
View More Questions
Top GATE NM Questions
- If \( \rightarrow \) denotes increasing order of intensity, then the meaning of the words [dry \( \rightarrow \) arid \( \rightarrow \) parched] is analogous to [diet \( \rightarrow \) fast \( \rightarrow \) \(\_\_\_\_\_\_\_\_\)]. Which one of the given options is appropriate to fill the blank?
- If two distinct non-zero real variables \( x \) and \( y \) are such that \( (x + y) \) is proportional to \( (x - y) \), then the value of \( \frac{x}{y} \) is:
- Consider the following sample of numbers: \[ 9, 18, 11, 14, 15, 17, 10, 69, 11, 13 \] The median of the sample is:
- The number of coins of ₹1, ₹5, and ₹10 denominations that a person has are in the ratio 5:3:13. Of the total amount, the percentage of money in ₹5 coins is:
- For positive non-zero real variables \( p \) and \( q \), if \[ \log \left( p^2 + q^2 \right) = \log p + \log q + 2 \log 3, \] then the value of \( \frac{p^4 + q^4}{p^2 q^2} \) is:
View More Questions