Question

In an examination, 30% of the students have failed in subject I, 20% of the students have failed in subject II and 10% have failed in both subject I and subject II. A student is selected at random, what is the probability that the student
a) has failed in subject I, if it is known that he has failed in subject II?
b) has failed in atleast one subject?
c) has failed in exactly one subject?

Answer 1

Answer:

a) 0.5

b) 0.4

c) 0.3

Step-by-step explanation:

Let F denote the event students failing in subject I

Given P(F) = 30% = 0.3

Let S denote the event students failing in subject II

Given P(S) = 20% = 0.3

Given that 10% have failed in both the subjects

P(F∩S) = 10% = 0.1

a) Probability that the student has failed in subject I, if it is known

that he has failed in subject II

= P(F/S)

= P(S∩F)/P(S)

= 0.1/0.2

= 1/2 = 0.5

b)probability that the student   has failed in at least one subject

= P(F∪S)

= P(F) + P(S) - P(F∩S)

= 0.3 + 0.2 - 0.1

= 0.4

c) probability that the student has failed in exactly one subject

= P(F ∪ S) - P(F ∩ S)

= 0.4 - 0.1

= 0.3

Hope, it helps !