Question

12. The blood groups of 50 students of a class are recorded as below.
Blood group
A
B
AB
O
Number of students
10
13
16
11
A student of the class is selected at random. What are the probabilities that the selected
student has the blood group (i) A, (ii) B and (iii) AB or O?​

Answer 1

Answer:

AB or O

Step-by-step explanation:

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Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

Total number of students = 50

So the total number of possible outcomes = 50

1.

A student of the class is selected at random

Let M be the event that the selected student has the blood group A

The number of students having blood group A is 10

Then the total number of possible outcomes for the event M is = 10

So the required probability

$\displaystyle \: P(M) = \frac{10}{50} = \frac{1}{5}$

2.

A student of the class is selected at random

Let N be the event that the selected student has the blood group B

The number of students having blood group B is 13

Then the total number of possible outcomes for the event N is = 13

So the required probability

$\displaystyle \: P(N) = \frac{13}{50}$

3.

Let S be the event that the selected student has the blood group AB

The number of students having blood group AB is 16

Then the total number of possible outcomes for the event S is = 16

$\displaystyle \: P(S) = \frac{16}{50} = \frac{8}{25}$

Let T be the event that the selected student has the blood group O

The number of students having blood group O is 11

Then the total number of possible outcomes for the event T is = 11

$\displaystyle \: P(S) = \frac{11}{50}$

Now

$S \cap \: T$

= the event that the selected student has the blood group AB & O

So The number of students having blood group AB & O is 0

Hence

$P(S \cap \: T) = 0$

So the required probability is

$P(S \cup \: T)$

$= P(S) + P(T) - P(S \cap T)$

$= \displaystyle \: \frac{8}{25} + \frac{11}{50}$

$= \displaystyle \: \frac{27}{50}$