Question

Two dice are thrown together. If the numbers appearing on the two dice are different, then what is the probability that the sum is $6?$
A. $\dfrac{5}{{36}}$
B. $\dfrac{1}{6}$
C. $\dfrac{2}{{15}}$
D. None of these

Answer 1

Hint:Probability can be defined as the state of being probable and the extent to which something is likely to happen in the particular situations or the favourable outcomes. Probability of any given event is given by the ratio of the favourable outcomes with the total number of the outcomes. Here we will first find the total possible outcomes and then the sum of the outcomes equal to the number six and then will calculate its probability.

Complete step by step answer:
Given that the two dice are thrown together.
Outcomes would be –
\[(1,1)\;{\text{(1,2) (1,3) (1,4) (1,5) (1,6)}} \\
\Rightarrow (2,1)\;{\text{(2,2) (2,3) (2,4) (2,5) (2,6)}} \\
\Rightarrow (3,1)\;{\text{(3,2) (3,3) (3,4) (3,5) (3,6)}} \\
\Rightarrow (4,1)\;{\text{(4,2) (4,3) (4,4) (4,5) (4,6)}} \\
\Rightarrow (5,1)\;{\text{(5,2) (5,3) (5,4) (5,5) (5,6)}} \\
\Rightarrow (6,1)\;{\text{(6,2) (6,3) (6,4) (6,5) (6,6)}} \\ \]
The total possible outcomes from the two thrown dices will be $ = 36$ ..... (A)
The favourable outcomes that are sum of the two dices should be equal to the number $6$
Favourable outcomes = $(1,5){\text{ (2,4) (3,3) (4,2) (5,1) }}$
The total number of favourable outcomes $ = 5$ .... (B)
The probability that A wills –
$\therefore P(A) = \dfrac{5}{{36}}$

Hence option A is the correct answer.

Note: Be good in identifying the correct favorable outcomes from the total possible outcomes. Always remember the probability of any event lies in between zero and one.When the probability is expressed in the form of the fraction then the denominator is always greater than or equal to the numerator.