Question

Following cards are put facing down $A,E,I,O,U$ what is the chance of drawing out
A) A Vowel
b) $A$ or $I$
c) A card marked $U$
d) A consonant

Answer 1

In this question we are given five cards that are put facing down and we have to find the probability or chance of given cases. First we will find the number of favourable outcomes in each case and the total number of outcomes is the same in each case then we will use the basic formula of probability to get our required answer.

Complete step-by-step solution:
Probability means how likely an event is to occur.
Formula of probability is
Probability of an event $=\dfrac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$
In a question it is given that we have $5$ cards named as $A,E,I,O,U$ . All the cards are put in such a way that they are facing down.
If we select or draw a card from these cards, we have to find the probability of drawing out the particular card.
a). A Vowel:
We have five cards named as $A,E,I,O,U$. In $26$ alphabets there are $5$ vowels that are $A,E,I,O,U$.
So,
Number of favourable outcomes $=5$
Total number of outcomes $=5$
Now we will use formula of probability
Probability of an event $=\dfrac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$
Probability or chance of getting a vowel
$\begin{aligned} & =\dfrac{5}{5} \\\ & = 1 \\\ \end{aligned}$
$\therefore 1$ Is the probability of getting a vowel from our given cards.
b). $A$ or $I$
We have five cards named as $A,E,I,O,U$.
There is one card of $A$ and one card of $I$ , so we have two options to select a card.
Now we will use formula of probability
Probability of an event $=\dfrac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$

So,
Number of favourable outcomes $=2$
Total number of outcomes $=5$
Probability or chance of getting a vowel
$\begin{aligned} & =\dfrac{2}{5} \\\ & = \dfrac{2}{5} \\\ \end{aligned}$
$\therefore \dfrac{2}{5}$ Is the probability of getting $A$ or $I$ from our given cards.
c). A card marked $U$
We have five cards named as $A,E,I,O,U$.
There is one card of $U$ , so we have only one option to select a card.
Now we will use formula of probability
Probability of an event $=\dfrac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$
So,
Number of favourable outcomes $=1$
Total number of outcomes $=5$
Probability or chance of getting a vowel
$\begin{aligned} & =\dfrac{1}{5} \\\ & = \dfrac{1}{5} \\\ \end{aligned}$
$\therefore \dfrac{1}{5}$ Is the probability of getting a card marked $U$ from our given cards.
d). A consonant
We have five cards named as $A,E,I,O,U$. In $26$ alphabets there are $5$ vowels that are $A,E,I,O,U$ and the rest $21$ are consonants.
Now we will use formula of probability
Probability of an event $=\dfrac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$
So,
Number of favourable outcomes $=0$
Total number of outcomes $=5$
Probability or chance of getting a vowel
$\begin{aligned} & =\dfrac{0}{5} \\\ & = 0 \\\ \end{aligned}$
therefore 0$ is the probability of getting a consonant from our given cards which means this is not possible to get consonant from given cards.

Note: Probability of an event can be $\left[ 0,1 \right]$ that is it can take any value between $0\And 1$ also including $0\And 1$ . If the probability of an event is $0$ which means that event is not possible and if the probability of an event is $1$ which means that event is certain or we can say that this event must occur.