Question

When two dice are thrown, then probability of getting equal number is:
A) 1/6
B) 1/2
C) 1/4
D) 1/3

Answer 1

Hint: Make the combinations of favourable events i.e. same number on both the dice and divide it to all the possible events that may be happened to get the probability of favourable event. Total events must always be greater than or equal to favourable events.

Formula used:
$P\left( A \right)=\dfrac{n}{e}$
Where $P\left( A \right)$the probability of any particular event is, $n$ is the number of events that are possible in the favour of $A$ event, $e$ is the total number of events that can be possible.
So total cases be like:
(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)
Now the same number on both dice have $6$events. And total event is $36$.
So $\Rightarrow P\left( A \right)=\dfrac{6}{36}$
$\Rightarrow P\left( A \right)=\dfrac{1}{6}$
Where $P\left( A \right)$ is the probability of the same number when two dice are thrown simultaneously.

Hence, option (A) is correct.

Additional information:
IF $X$ number of dice are thrown. Where $X$ is any natural number. Then total cases possible is ${{6}^{X}}$. Value of any probability is always less than 1.

Note: Count the events carefully to avoid the error, check your answer that’s not greater than 1. Because the probability of anything can’t be greater than one and less than zero. In an unbiased dice six face has equal probability to come on top.