Question

In a class of 100 students. 60 student drink tea ,50 student drink coffee and 30 students drink both tea and coffee . a student from this class is sellected at random. find the probavility thet the students takes at leastons of the two drinks

Answer 1

In a class of 100 students, 60 student drink tea, 50 student drink coffee and 30 students drink both tea and coffee. A student from this class is selected at random.

To find the probability that the students takes at least one of the two drinks.

Now this question can be solved using Venn Diagram. A Venn diagram is shown below.

• 'a' represents the set of students who ONLY drink tea
• 'c' represents the set of students who ONLY drink coffee.
• 'b' represents the set of students who drink BOTH tea and coffee which is equal to 30.
• T representing the set of students who drink tea i.e. (a + b).
• C representing the set of students who drink coffee i.e. (b + c).

Here, n(T) = 60, n(C) = 50.

So, the no. of students who drink only tea, a = 60 - 30

                                                                          = 30

The no. of students who drink only coffee, c = 50 - 30

                                                                          = 20

So the no. of students drink at least one of the two = T U C

                                                                                      = a+b+c

                                                                                      =30+30+20 = 80

Now, no. of total outcomes = 100

And no. of favorable outcomes = 80

So, probability that the student takes at least one of the two drinks = 80/100

=0.8 , which is equal to 80%.

So, probability that the student takes at least one of the two drinks is 0.8.

Answer 2

Probability of randomly selecting a student who takes at least one drink = 0.8

Step-by-step explanation:

Given :

Total number of students in class = 100

Number of students who drink tea = 60

Number of students who drink coffee = 50

Number of students who drink  both tea and coffee = 30

To find the probability of of selecting a student randomly who takes at least one of the two drinks.

Solution:

Number of students who drink only tea = $60-30=30$

Number of students who drink only coffee = $50-30=20$

Number of students who take both drinks = 30

Total number of students who take at least one drink = $30+20+30=80$

Probability of selecting a student at random who takes at least one drink can be given as:

⇒ $\frac{Number\ of\ students\ taking\ at\ least\ one\ drink}{Total\ number\ of\ students}$

⇒ $\frac{80}{100}$

⇒ $0.8$