100 students appeared for two examinations. 60 passed the first, 50 passed the second and 30 passed both. find the probability that a student selected at random has failed in the both the examinations?
Answers
Probability of Passing second exam=1/2
Both =3/10
Failing both=1-P(AUB)
=1-(3/5+1/2-3/10)
=4/5
Answer:
Probability that a student selected at random failed in both the examination = 1/5
Explanation:
Total number of student given are 100.
Number of student passed in first examination is 60. So, probability of student passing in first examination is, P(A) = = 60/100
Number of student passed in second examination is 50. So, probability of student passing in second examination is, P(B) = = 50/100
Number of student passed in both examination is 30. So, probability of student passing in both examination is, P(A ∩ B) = = 30/100
From probability addition rule,
P(A ∪ B) = P(A) + P(B) - P(A∩B)
P(A ∪ B) = 60/100 + 50/100 - 30/100
P(A ∪ B) = 80/100
Thus, probability of student passing at least in one subject is 80/100.
Probability of student failing in both subject is given by,
P(A∪ B)' = 1 - P(A ∪ B)
= 1 - 80/100
= 1/5
Thus, Probability of student failing in both subjects are 1/5.
Hope it helps.....