Question

A dice is thrown twice. The probability that 5 will not come up either time is:

• A. $ \frac{11}{36} $
• B. $ \frac{25}{36} $
• C. $ \frac{13}{36} $
• D. $ \frac{17}{36} $

Hint:

For independent events, the probability of multiple events occurring together is the product of their individual probabilities. When calculating the probability of an event not happening, use the complement rule: $ P(\text{Not Event}) = 1 - P(\text{Event}) $.

Answer 1

The Correct Option is B

Step 1: Understand the Problem.
When a die is thrown, there are 6 possible outcomes: \{1, 2, 3, 4, 5, 6\}.
The probability of rolling a 5 on a single throw is: \[ P(5) = \frac{1}{6}. \] The probability of not rolling a 5 on a single throw is: \[ P(\text{Not 5}) = 1 - P(5) = 1 - \frac{1}{6} = \frac{5}{6}. \] Step 2: Calculate the Probability for Two Throws.
Since the throws are independent events, the probability that 5 does not come up on either throw is: \[ P(\text{Not 5 on both throws}) = \left(\frac{5}{6}\right) \times \left(\frac{5}{6}\right) = \frac{25}{36}. \] Step 3: Analyze the Options.
Option (1): \( \frac{11}{36} \) — Incorrect, as this does not match the calculated value.
Option (2): \( \frac{25}{36} \) — Correct, as it matches the calculated value.
Option (3): \( \frac{13}{36} \) — Incorrect, as this does not match the calculated value.
Option (4): \( \frac{17}{36} \) — Incorrect, as this does not match the calculated value. Step 4: Final Answer.
\[ (2) \quad \frac{25}{36} \]