Question

Three persons Mr. Bhose, Mrs. Ali , and Mr. Chowdhury are being considered for the appointment as Vice-Chancellor of a University whose chance of being selected for the post are in the proportion 4: 3: 2 respectively. The probability that Mr. Bhose, if selected, will introduce compulsory English course is 0.5, the corresponding probabilities for Mrs. Ali and Mr. Chowdhury doing the same are, respectively, 0.6 and 0.7. What is the probability that compulsory English course would be introduced in the university?​

Answer 1

Answer:

Probability = 0.572

Step-by-step explanation:

Given:

The probability that Mr.Bhose, Mrs.Ali and Mr.Chowdhury would be selected for the post are in the ratio 4:3:2

The probability that if selected, Mr..Bhose, Mrs.Ali and Mr.Chowdhury would introduce compulsory English course is 0.5, 0.6, 0.7 respectively

To Find:

The probability that compulsory English course would be introduced in the university

Solution:

Let E₁, E₂, E₃ be the events of Mr..Bhose, Mrs.Ali and Mr.Chowdhury getting selected for the post respectively.

P(E₁) = 4/9 = 0.44

P(E₂) = 3/9 = 0.33

P(E₃) = 2/9 = 0.22

Now let A be the event that compulsory English is introduced in the university.

Hence by given,

P(A/E₁) = 0.5

P(A/E₂) = 0.6

P(A/E₃) = 0.7

Now the probability that the course has been introduced is given by,

$\sf P(A)=P\bigg((E_1\cap A)\cup (E_2\cap A)\cup (E_3\cap A)\bigg) \\ \\ \\ \sf \implies P(E_1\cap A)+P(E_2\cap A)+P(E_3\cap A) \\ \\ \\ \sf \implies P(E_1)\times P(A/E_1)+P(E_2)+P(A/E_2)+P(E_3)+P(A/E_3) \\ \\ \\ \sf \implies 0.44\times0.5+0.33\times 0.6+0.22\times 0.7 \\ \\ \\ \sf \implies 0.22+0.198+0.154 \\ \\ \\ \sf \implies 0.572$

Hence the probability that English course would be introduced is 0.572.