Question

In the sample of 50 people, 21 has type “O” blood, 22 has type “A” blood, 5 has type “B” blood and 2 has type “AB” blood. If a person is selected at random, find the probability that the person does not have type “AB” blood.
A.\[\dfrac{{24}}{{25}}\]
B. \[\dfrac{2}{{25}}\]
C. \[\dfrac{{14}}{{25}}\]
D. None of these

Answer 1

Hint: Here we use the concept of probability to find the required probability. Find the total number of people by adding the number of people with different blood types.
* Probability of an event is given by dividing the number of favorable outcomes by total number of outcomes.

Complete step by step solution:
We are given that
Number of people with blood type “O” \[ = 21\]
Number of people with blood type “A” \[ = 22\]
Number of people with blood type “B” \[ = 5\]
Number of people with blood type “AB” \[ = 2\].....................… (1)
We calculate the total number of people from the given data by adding the number of people of each of the blood types “O”, “A”, “B” and “AB”.
\[ \Rightarrow \]Total number of people \[ = 21 + 22 + 5 + 2\]
\[ \Rightarrow \]Total number of people \[ = 50\].....................… (2)
Now we know Probability of an event is given by dividing the number of favorable outcomes by the total number of outcomes.
We have to choose a person without blood type “AB” so a favorable outcome is the number of people without blood type “AB”. Also, total outcomes are the number of total people which are given by equation (2).
Here the number of favorable outcomes is 48 and the total number of outcomes is 50.
\[ \Rightarrow \]Probability\[ = \dfrac{48}{{50}}\]
Cancel same factors from numerator and denominator
\[ \Rightarrow \]Probability\[ = \dfrac{24}{{25}}\]
\[\therefore \]Probability that chosen person from the total people without blood type “AB” is \[\dfrac{24}{{25}}\]

\[\therefore \]Correct option is A.

Note: Students are likely to leave the probability in fraction without cancelling the same factors from numerator and denominator. Keep in mind probability should always be in smallest and simplest form that means there should be no common factor between numerator and denominator. Probability of an event always lies between 0 and 1.