Two biased dice are rolled. Out of which one die contains 1, 1, 2, 2, 3, 3, and another die contains 1, 2, 2, 3, 3, 4. Then the probability of getting a sum of 4 or 5 is:

Question

Let \(y=y(x)\) be the solution of the differential equation \[ x\frac{dy}{dx}=y-x^2\cot x,\quad x\in(0,\pi) \] If \(y\!\left(\frac{\pi}{2}\right)=\frac{\pi^2}{2}\), then \[ 6y\!\left(\frac{\pi}{6}\right)-8y\!\left(\frac{\pi}{4}\right) \] is equal to:

Answer 1

The probability of obtaining a sum of 4 or 5 when rolling two dice is to be determined. The outcomes yielding a sum of 4 are (1, 3), (2, 2), and (3, 1), totaling 3. The outcomes yielding a sum of 5 are (1, 4), (2, 3), (3, 2), and (4, 1), totaling 4. The aggregate number of favorable outcomes is 3 + 4 = 7. The total possible outcomes from rolling two dice equate to \( 6 \times 6 = 36 \). Consequently, the probability is \( \frac{7}{36} \). Therefore, the correct probability is \( \frac{7}{36} \).

Two biased dice are rolled. Out of which one die contains 1, 1, 2, 2, 3, 3, and another die contains 1, 2, 2, 3, 3, 4. Then the probability of getting a sum of 4 or 5 is:

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The Correct Option is C

Solution and Explanation

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