1. In 2021 there will be 3 candidates for the post of Director- Mr. Arun, Mr....

1. In 2021 there will be 3 candidates for the post of Director- Mr. Arun, Mr. Varun, and Mr.
Tharun- whose chances of getting the appointment are in the proportion 3: 2: 4 respectively.
The probability that Mr. Arun if selected would introduce online-teaching in the college is
0.3. The probabilities of Mr. Varun and Mr. Tharun doing the same are respectively 0.5 and
0.8. (a) What is the probability that there will be online-teaching in the college in 2022? (b) If
there is online-teaching in the college in 2022, what is the probability that Mr. Tharun is the

Solutions

Expert Solution

Solution :

Let us define some events as follows :

A : Mr. Arun will get the appointment

B : Mr. Varun will get the appointment

C : Mr. Tharun will get the appointment

D : There will be online-teaching in the college

The proportion of getting appointment for Arun, Varun and Tharun is 3:2:4.

Total = (3 + 2 + 4) = 9

Hence, P(A) = 3/9 = 1/3, P(B) = 2/9, P(C) = 4/9

Also we are given following informations :

P(D | A) = 0.3, P(D | B) = 0.5, P(D | C) = 0.8

a) We have to find P(D).

The event D will occur if either A and D occur or B and D occur and C and D occur.

P(D) = P(A ∩ D) + P(B ∩ D) + P(C ∩ D)

P(D) = P(D | A).P(A) + P(D | B).P(B) + P(D | C).P(C)

P(D) = (0.3 × (1/3)) + (0.5 × (2/9)) + (0.8 × (4/9))

P(D) = 0.1 + 0.1111 + 0.3556

P(D) = 0.5667

The What is the probability that there will be online-teaching in the college in 2022 is 0.5667.

b) We have to find P(C | D).

If there is online-teaching in the college in 2022, the probability that Mr. Tharun is appointed is 0.6275.

orchestra answered 1 year ago

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