Question

Given a fair six-faced dice where the faces are labelled ‘1’, ‘2’, ‘3’, ‘4’, ‘5’, and ‘6’, what is the probability of getting a ‘1’ on the first roll of the dice and a ‘4’ on the second roll?

• A. $\dfrac{1}{36}$
• B. $\dfrac{1}{6}$
• C. $\dfrac{5}{6}$
• D. $\dfrac{1}{3}$

Hint:

When two independent events occur in sequence, multiply their individual probabilities.

Answer 1

The Correct Option is A

Step 1: Probability of first event.
The probability of rolling a ‘1’ on a fair six-faced die is: \[ P(\text{getting 1}) = \frac{1}{6} \]
Step 2: Probability of second event.
The probability of rolling a ‘4’ on the second roll is also: \[ P(\text{getting 4}) = \frac{1}{6} \]
Step 3: Apply multiplication rule of independent events.
The rolls are independent events. Therefore, \[ P(\text{1 on first AND 4 on second}) = \frac{1}{6} \times \frac{1}{6} = \frac{1}{36} \] Final Answer: \[ \boxed{\dfrac{1}{36}} \]