Question

manager has given a task to four employees A, B, C, D. The chances of completion of the task on time are ⅔, ¼, ⅕, and ⅙ respectively. What is the probability that the task will get completed on time?

Answer 1

let,

A= event that task is given to employee A

B= event that task is given to employee B

C= event that task is given to employee C

D= event that task is given to employee D

T= event that task is completed on time.

Now, According to question,

P(A) = P(B) = P(C) = P(D) = $\frac{1}{4}$

[ using the concept of conditional probability i.e. P($\frac{A}{B}$) means probability of event A occuring given that event B occurs ]

P($\frac{T}{A}$) = $\frac{2}{3}$

P($\frac{T}{B}$) = $\frac{1}{4}$

P($\frac{T}{C}$) = $\frac{1}{5}$

P($\frac{T}{D}$) = $\frac{1}{6}$

So,

P(T)= $\frac{1}{4}$*$\frac{2}{3}$ +  $\frac{1}{4}$* $\frac{1}{4}$ +  $\frac{1}{4}$*$\frac{1}{5}$ + $\frac{1}{4}$*$\frac{1}{6}$ = $\frac{40+15+12+10}{240}$ = $\frac{77}{240}$ = 0.32

Hence, the required probability is 0.32.

Answer 2

Answer:

The probability that the task will get completed on time = 5/6

Step-by-step explanation:

For the task to be completed on time

following tests are possible ,

1). If all A,B,C,D works ....

2). If any one of A,B,C,D does not work.

3). If any two of A,B,C,D do not work.

4). If any three of A,B,C,D do not work.

5). the task will not be complete if no one will work.

hence we can subtract the 5th case from the whole probability that will ensure that the work will be done on time.

hence :

1. Chances of A , that he will not do the task = P(A*) = 1-P(A) = 1 - 2/3 = 1/3

2. Chances of B , that he will not do the task = P(B*) = 1-P(B) = 1 - 1/4 = 3/4

3. Chances of C , that he will not do the task = P(C*) = 1-P(C) = 1 - 1/5 = 4/5

4. Chances of D , that he will not do the task = P(D*) = 1-P(D) = 1 - 1/6 = 5/6

Hence ,the probability that the task will get completed

on time =  1 - P(A*) x P(B*) x P(C*) x P(D*) = 5/6

#SPJ3