Question

in a certain college, 25% of the students failed mathematics,15% of the students failed chemistry and 10% of the students failed both mathematics and chemistry. A student is selected at random,
I)if he failed the exam, what is the probability that he failed mathematics?
ii) if he failed mathematics, what is the probability that he failed chemistry?
iii) what is the probability that he failed mathematics or chemistry?

Answer 1

In a certain college , 25% of the students failed in mathematics,15% of the students failed in chemistry and 10% of the students failed in both mathematics and chemistry .

Let us denote the event of failing in mathematics by M,and the event of failing in chemistry by C.

Then,

P(M)=25/100=0.25

P(C)=15/100=0.15

P(M and C)=10/100=0.10

A student is selected at random.

i)

If he failed the exam,what is the probability that he failed in maths ?

I think this question is a bit wrong,and it would be 'if he failed in chemistry'(Let me know if it is not)

So,

P(M/C)

=P(M and C)/P(C)

=0.10/0.15

=0.666

ii)

If he failed in maths , what is the probability that he failed in chemistry ?

So,

P(C/M)

=P(C and M)/P(M)

=0.10/0.25

=0.4

iii)

What is the probability that he failed in maths or chemistry ?

So,

P(C or M)

=P(M)+P(C)-P(C and M)

=0.25+0.15-0.10

=0.40-0.10

=0.30