Question

Hundred students appeared for two examinations. 60 passed the first, 50 passed the second and 30 passed in both. Find the probability that student selected at random
a) passed in at least one examination
b) passed in exactly one examination
c) failed in both the examinations.

Answer 1

Answer:

a) 4/5

b) 1/2

c) 1/5

Step-by-step explanation:

Hi,

Given total number of students who appeared for test = 100

Let F be event student passing the first test,

P(F) : probability that students pass the first test = 60/100 = 3/5

Let S be event student passing the second test

P(S) : probability that students pass the second test = 50/100 =

1/2

Let S∩F be the event that students pass both the tests

P(S∩F): probability that student passes both the tests = 30/100 =

3/10

a) Probability that students passed in atleast one examination

= P(F∪S) = P(F) + P(S) - P(F∩S)

= 3/5 + 1/2 - 3/10

= 4/5

Hence probability that student selected at random passed in

at least one examination is 4/5.

b)Probability that student passes in exactly one examination

= P(F ∪ S) - P(F ∩ S)

= 4/5 - 3/10

= 1/2

Hence, probability that student passed in exactly one

examination is 1/2

c) Probability that student failed in both the examinations is

1 - P(F ∪ S)

= 1 - 4/5

= 1/5

Hence, probability that the student failed in both the

examinations is 1/5

Hope, it helps !