Question

In Mr. ERIZ’s class, the probability of student who likes Mathematics subject is 0.5 and the probability who likes both Mathematics and Statistics subjects is 0.25.

1. If one student is chosen at random, what is the probability that this student likes Statistics given that he/she also like Mathematics subject?
2. If the probability of students who likes Statistics is 0.45, are the events ‘like Mathematics subject’ and ‘like Statistics subject’ independent? Justify your answer. (4 marks)
3. Are the events ‘likes Mathematics’ and ‘likes Statistics’ mutually exclusive? Justify your answer. (2 marks)

Answer 1

i) P(Likes Statistics | Also like Maths)

= P(Likes both) / P(Likes Math)

= 0.25 / 0.50

= 0.50

ii) From part a), P(Likes Statistics | Also like Maths) = 0.50

And

P(Likes Statistics) = 0.45

Since both these quantities are not equal, events ‘like Mathematics subject’ and ‘like Statistics subject’ are not independent.

iii) No, events ‘likes Mathematics’ and ‘likes Statistics’ are not mutually exclusive because they both can occur at the same time with probability = 0.25

Answer 2

i)

M=event that a student likes mathematics.

S=event that a student likes statistics.

P(M) =0.5

P(M  S) =0.25

So, P(S|M) = P(MS) /P(S) =0.25/0.5=0.5

ii)

P(S) =0.45

If they are independent then P(M S) shoud be equal to P(S) *P(M)

But P(S) *P(M) =0.5*0.45=0.225  0.25

So, these 2 events are not independent.

iii)

If these 2 events are mutually exclusive then P(MS) should be 0.

But here P(MS) =0.25

So, these 2 events are not mutually exclusive.

answered by: MAA