A 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?

Answers 2

Answer:

If the probability that a problem will be solved by three people is 1/2, 1/3 and 1/6, then what is the probability that the problem will be solved?

Probability of A solving the problem = P(A) = 1/2

Probability of B solving the problem = P(B) = 1/3

Probability of C solving the problem = P(C) = 1/6

Problem will be solved when i) either one of A, B, C solve the problem, ii) two of A, B, C solve the problem, OR iii) all of A, B, C solve the problem

Problem will not be solved when - all of A, B, C are not able to solve the problem

Probability of A not solving the problem = P(A) = 1/2

Probability of B not solving the problem = P(B) = 2/3

Probability of C not solving the problem = P(C) = 5/6

Probability of problem not being solved = A, B, C not solving the problem simultanously = P(A)*P(B)*P(C) = (1/2)*(2/3)*(5/6)

= 5/18

Probability of problem being solved = 1 - probability of problem not being solved

= 1 - (5/18) = 13/18

Answer:

The probability of completing the task on time is 5/6

Step-by-step explanation:

Given the probabilities of completion of a task by the employees

A, P(A) = 2/3

B, P(B) = 1/4

C, P(C) = 1/5

D, P(D) = 1/6

Now if we compute the probabilities of not completing a task we get

P'(A) = 1/3

P'(B)  = 3/4

P'(C) = 4/5

P'(D) = 5/6

The task will not be completed if none of them is complete the task on time.

P(not completing the task) = 1/3x3/4x4/5x5/6 = 1/6

Now the probability of completing the task is 1-1/6 = 5/6

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