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:

For multiple independent events, multiply individual probabilities for "AND" questions. If it had been "OR", use addition with inclusion–exclusion.

Answer 1

The Correct Option is A

Step 1: Identify sample space per roll.
A fair die has 6 equally likely outcomes, so for any specified face $k\in\{1,\dots,6\}$, $P(\text{roll}=k)=\dfrac{1}{6}$.

Step 2: Compute each required single-roll probability.
$P(\text{first roll} = 1)=\dfrac{1}{6}$, $P(\text{second roll} = 4)=\dfrac{1}{6}$.

Step 3: Use independence of successive rolls.
The two rolls are independent, so the joint probability equals the product:
\[ P(\text{first}=1 \ \text{AND}\ \text{second}=4)=\frac{1}{6}\times\frac{1}{6}=\frac{1}{36}. \] \[ \boxed{\dfrac{1}{36}} \]