Question

The blood groups of 30 students of class VIII are recorded as follows
A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O,
A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O.
Use this data to determine the probability that a student of this class, selected at random, has blood group AB.

Answer 1

Here to solve the given problem we have to remember that that total number of outcomes is equal to the number of students present. To find out the probability of a desired outcome we are provided with the formulae
$P(A)$ = $\dfrac {n(E)}{n(S)}$
Where,
P(A) = Probability of an event
n(E) = Number of desired outcome
n(S) = Total number of outcomes

Complete step-by-step solution:
First, as we know that total number of students in class = Total number of outcomes
i.e. n(S) = 30
Then the number of students having blood group AB = Number of desired outcomes
i.e. n(E) = 3
If we assume P(A) to be the probability of selecting a student randomly from the class of 30 students, having blood group AB
Then by using the formulae $P(A)$ = $\dfrac {n(E)}{n(S)}$
We substitute the values of n(E) and n(S) from step 1 and step 2,and we get
P(A) = $\dfrac{3}{\begin{gathered} 30 \\\ \\\ \end{gathered} }$
P(A) = $\dfrac{1}{{10}}$
Therefore, P(A) i.e. Probability of selecting a student randomly from the class VIII having blood group AB = $\dfrac{1}{{10}}$

Note: The probability of AB blood group is lowest among all types of blood groups while the O type blood group has highest probability among all the types of blood group in this question. So can be asked this way which blood group has the highest probability and which has highest.