Question

16 people study French, 21 study Spanish and total number of students studying these languages is 30. Consider the experiment of radomnly selecting students and the events X and Y defined as
X = {Student studying French is selected}
Y = {Student studying Spanish is selected}
X and Y are mutually exclusive events.

• A. True
• B. False

Answer 1

The correct option is B False

Number of people studying French = 16
For Spanish it is 21.
If you add them it comes out to be 37.
But total number of students is 30. Right? What does this mean? This means (37-30) = 7 students are studying both the languages. These are counted both in French ones and Spanish ones.
That means $X\cap Y=7\ne 0$
So these 7 elements are common to both the events.
So X and Y are not mutually exclusive.