GATE Electrical 2023 | GA | Question: 3

Question

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

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

Answer 1

We have a fair six-sided die. When we roll it:

• There's a $1$ in $6$ chance $(1/6$ probability) of getting a '$1$' on the first roll.
• There's also a $1$ in $6$ chance $(1/6$ probability) of getting a '$4$' on the second roll.

Since these rolls are independent events, meaning one doesn't affect the other, we can multiply the probabilities:

$(1/6) * (1/6) = 1/36$

So, the probability of rolling a '$1$' on the first roll and a '$4$' on the second roll is $1/36.$

Correct Answer: A

Answer 2

TOTAL CASES = 6^6
FAV CASES = 1*6*6*1*6*6  = 6^4
P = 1/36