Question

The six faces of a die are marked as A, B, C, D, E and F. The event M is getting a vowel on the upper face of the die when it is tossed. The probability of the event M is
a) 1
b) ½
c) 1/3
d) 2/3

Answer 1

Hint: The probability of an event is equal to $\dfrac{\text{total no}\text{. of favorable outcomes}}{\text{total no}\text{. of outcomes}}$.

Complete step-by-step answer:

It is given here that a die has six faces named as A, B, C, D, E and F and the event M is getting a vowel on the upper face of the die.

Now, the probability of an event is given as the ratio of the total no. of favorable outcomes to the total no. of outcomes, i.e. $\dfrac{\text{total no}\text{. of favorable outcomes}}{\text{total no}\text{. of outcomes}}$.

Here, it is given that the event M is getting a vowel out of A, B, C, D, E and F on the upper face of the die when it is tossed.

So, the favorable outcomes for event M are A and E i.e. there are two favorable outcomes.
The total outcomes are A, B, C, D, E and F. That is the total number of outcomes is 6.

So, the probability of event M (P(M)) = $\dfrac{\text{total no}\text{. of favorable outcomes}}{\text{total no}\text{. of outcomes}}$= $\dfrac{2}{6}$ = $\dfrac{1}{3}$

Hence, we get our answer as $\dfrac{1}{3}$.

Therefore, the correct option to the question out of the four options is option (c) $\dfrac{1}{3}$.

Note: While calculating the probability, we should find out the number of favorable outcomes which will be the number of events satisfying the given conditions. In this case the condition was the letter being a vowel, therefore, it was satisfied only by A and E. In other questions, the condition can be different and thus the favorable outcomes will be decided accordingly.