Question

Two dice are thrown simultaneously. The probability of obtaining a total score of $5$ is
(1) $\dfrac{1}{9}$
(2) $\dfrac{1}{{18}}$
(3) $\dfrac{1}{{36}}$
(4) $\dfrac{1}{{12}}$

Answer 1

Hint : The given question is based on probability. Probability deals with the occurrence of a random event. In this question we are asked to find the occurrence of obtaining total $5$ while throwing two dice. To find the probability let find the favourable outcomes.

Complete step-by-step answer :
In this question two dice are thrown. If one dice is thrown then the possible outcome is $6$because, a dice has $6$faces with numbers from $1{\text{ to }}6$, that is, $(1),(2),(3),(4),(5),(6)$
If two dice are thrown then the possible outcome is $6 \times 6 = 36$.
The possible outcomes are:Let as assume the sample space for rolling a pair of dice are mentioned in the table is given below:

Here we need only the outcomes of the sum of $5$.
Then the possible outcome will be $(1,4),(2,3),(3,2){\text{ and }}(4,1)$
The number of possible outcomes is $4$ out of $36$.
Probability of obtaining total score $5$, P($5$) $= \dfrac{4}{{36}}$
By cancelling both by $4$, we will get, $\dfrac{1}{9}$.
Probability of obtaining total score $5$, P($5$) $= \dfrac{1}{9}$.
Hence, option (1) $\dfrac{1}{9}$ is correct.
So, the correct answer is “Option 1”.

Note : Probability means possibility.
When a dice is thrown, the number appearing on its upper face is the favourable outcome. In one dice, the probability of getting any number or favourable outcome is $\dfrac{1}{6}$.
If two dice are thrown simultaneously and the numbers appearing on the dice are noted. Total number of outcomes is $36$.
The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of outcomes and the total number of outcomes.
Probability of happening of any event,
$P(A) = \dfrac{{{\text{Possible outcomes}}}}{{{\text{Total number of outcomes}}}}$ .