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

We will create a sample space and find the probability of each of the events by taking a ratio of the number of favorable outcomes to the total number of outcomes in the sample space. For each event, the sample space will remain the same.

Complete step-by-step solution:
The formula to find probability is
${\text{P(event) = }}\dfrac{{{\text{number of favorable outcomes}}}}{{{\text{total number of outcomes in sample space}}}}$
The sample space is $S = \\{ A,E,I,O,U\\}$
The number of outcomes in sample space is $n(S) = 5$
a) Let the event for drawing out a vowel be ${E_1}$
$\therefore {E_1} = \\{ A,E,I,O,U\\}$
The number of outcomes of ${E_1}$ is $n({E_1}) = 5$
The probability of drawing out a vowel from the sample space will be
$P({E_1}) = \dfrac{{n({E_1})}}{{n(S)}}$
$\therefore P({E_1}) = \dfrac{5}{5} = 1$
The probability of drawing out a vowel from the sample space will be $1$ .
b) Let the event for drawing out A or I be ${E_2}$
$\therefore {E_2} = \\{ A,I\\}$
The number of outcomes of ${E_2}$ is $n({E_2}) = 2$
The probability of drawing out A or I from the sample space will be
$P({E_2}) = \dfrac{{n({E_2})}}{{n(S)}}$
$\therefore P({E_2}) = \dfrac{2}{5}$
The probability of drawing out A or I from the sample space will be $\dfrac{2}{5}$ .
c) Let the event for drawing out A card marked U be ${E_3}$
$\therefore {E_3} = \\{ U\\}$
The number of outcomes of ${E_3}$ is $n({E_3}) = 1$
The probability of drawing out A card marked U from the sample space will be
$P({E_3}) = \dfrac{{n({E_3})}}{{n(S)}}$
$\therefore P({E_3}) = \dfrac{1}{5}$
The probability of drawing out A card marked U from the sample space will be $\dfrac{1}{5}$.
d) Let the event for drawing out A consonant be ${E_4}$
$\therefore {E_4} = \\{ \\}$
The number of outcomes of ${E_4}$ is $n({E_4}) = 0$
The probability of drawing out A consonant from the sample space will be
$P({E_4}) = \dfrac{{n({E_4})}}{{n(S)}}$
$\therefore P({E_4}) = 0$
The probability of drawing out A consonant from the sample space will be $0$ .

Note: The probability of an event is а number (аlwаys positive) that represents the сhаnсes of оссurrenсe of an event. The probability range of an event is between zero and one. The probability of an imроssible event is zero whereas the probability of а роssible event is one.