For the first one, yes.
But for the other two... can I ask you how you got those answers?
Of 500 students , 200 participating in math activity , 250 participating in science activity and 50 participated in both activities , Find that a randomly selected student.
a) Will be a participant in at least one of the two activities.
b) Will not be a participant in either activity.
c) Will be a participant in exactly one activity.
My answer :
a) 0.8
b) 0.3
c) 0.5
Is my answer correct?
b). Ah, there is your mistake. The probability that the student will not be a participant in either activities is:
Drawing a Venn Diagram might be easier to follow.
c). Here also, a Venn Diagram would show you the right answer. You didn't remove the set
Let me show you the Venn Diagram:
You will immediately see that those who will not be participant in either activities is 100 over 500.
And for c), it becomes (150 + 200)/500 = 0.7
They are those which aren't in any of the sets.
You know that 50 students perform both, hence the 50 in the intersection of the sets.
You know a total of 200 perform in math, hence, 150 performed only math.
You know a total of 250 perform in science, hence, 200 performed only science.
Total up to now is 150 + 50 + 200 = 400
which means, 100 of them don't do either.
The probability then becomes obvious.