Question

In a sample survey of $640$ people, it was found that $400$ people have a secondary school certificate. If a person is selected at random, what is the probability that the person does not have such a certificate?
A. $0.375$
B. $0.625$
C. $0.725$
D. $0.875$

Answer 1

Probability is 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 equal to the ratio of the favourable outcomes with the total number of the outcomes.
P(A) = Total number of the favourable outcomes (BY) Total number of the outcomes

Complete answer:
Let A be an event where the person does not have a Secondary certificate.
In the sample survey we are given $640$ people and it was found that $400$ have the secondary certificate.
Now the number of people do not having certificate is $n(A) = 640 - 400 = 240$
Total number of people in the survey is $n(S) = 640$
Now, the probability can be given by $P(A) = \dfrac{{n(A)}}{{n(S)}}$
Place the values in the above equation,
$\Rightarrow P(A) = \dfrac{{240}}{{640}}$
Find division for the term on the right hand side of the equation,
$\Rightarrow P(A) = 0.375$
Hence, from the given multiple choices, the option A is the correct answer.
So, the correct answer is “Option A”.

Note: While solving the probability problems read the question twice and note down the given and unknown and find the correlation. The probability of any event always ranges between zero and one. It can never be the negative number or the number greater than one. The probability of impossible events is always equal to zero whereas, the probability of the sure event is always equal to one.