Question

Given a fair six-faced die (faces labelled 1–6), what is the probability of getting a '1' on the first roll and a '4' on the second roll?

• A. \(\tfrac{1}{36}\)
• B. \(\tfrac{1}{6}\)
• C. \(\tfrac{5}{6}\)
• D. \(\tfrac{1}{3}\)

Hint:

When events are independent, multiply their probabilities. For two specific outcomes in dice rolls, always compute \((\tfrac{1}{6})(\tfrac{1}{6})=\tfrac{1}{36}\).

Answer 1

The Correct Option is A

Step 1: Probability of first roll.
The die has 6 equally likely outcomes. Probability of rolling a 1 = \(\tfrac{1}{6}\).

Step 2: Probability of second roll.
Independence: the second roll is not affected by the first. Probability of rolling a 4 = \(\tfrac{1}{6}\).

Step 3: Combine independent events.
The probability of both happening = \(\tfrac{1}{6}\times\tfrac{1}{6}=\tfrac{1}{36}\).

Final Answer:
\[ \boxed{\tfrac{1}{36}} \]