Question

An unbiased die is thrown. What is the probability of getting an even number or a multiple of 3?

Answer 1

Hint- First make the sample space i.e. Total no. Of possible outcomes when a dice is thrown. Then differentiate how many outcomes are even numbered and how many are odd. Then find the probability of even no., probability of multiple of three, probability of even and multiple of three and do the calculations.

Complete step-by-step answer:
In a single throw of an unbiased dice, we can get any one of the outcomes: 1,2,3,4,5 or 6
So, exhaustive number of cases=6
Case.1 An even number is obtained if we obtain any one of 2,4,6 as an outcome.
So, favourable number of cases = 3.
Thus, required probability = \[\dfrac{3}{6} = \dfrac{1}{2}\]
Case.2 A multiple of 3 is obtained if we obtain anyone of 3,6 as an outcome.
So, favourable number of cases = 1
Thus, required probability = \[\dfrac{2}{6} = \dfrac{1}{3}\]
Case.3 An even number and a multiple of 3 is obtained in any of the following outcomes 2,3,4,6.
So, favourable number of cases = 4.
Thus, required probability = \[\dfrac{4}{6} = \dfrac{2}{3}\]
Case.4 An even and a multiple of 3 is obtained if we get 6 as an outcome.
So, favourable number of cases = 1.
Thus, required probability = \[\dfrac{1}{6}\]

Note- The ratio of no. of favourable outcomes to the total no. of possible outcomes is called probability. Sample space of the random trail is the set of all the possible outcomes. In the above questions the no.appeared on the dice when thrown makes the sample space.