Problem 1 Historical data suggests that a scientific journal

Problem 1. Historical data suggests that a scientific journal accepts 5% of the manuscripts it receives, rejects 50% of the manuscripts it receives, and requests revise and resubmit for the remaining manuscripts. In a given month, the journal receives 75 manuscripts. (a) What is the probability that 5 are accepted and 40 are rejected? (h) What is the probability that 5 are accepted? (c) What is the probability that 40 are rejected given that 5 are accepted?

Solution

let A represents manuscripts accepted

let B represents manuscripts rejected

let C be the manuscripts revise and resubmit

probability of accepting manuscript p = 0.05

probability of rejecting manuscript q = 0.5

probability of revise r = 0.45

a)

probability 5 are accepted and 40 are rejected is

P(A=5 and B=40) = 75!/(5! *40!* 30!) (0.05)^5 (0.5)^40 (0.45)^30

= 0.0107 or 1.07%

b)

probability that 5 are accepted

P(A=5) = 75!/(5! * 70!) (0.05)^5 (0.95)^70

= 0.1488 or 14.88%

c)

probability that 40 are rejected given 5 are accepted

using conditional probability rule

P(B=40/A=5) = P(B=40 and A=5) / P(A)

= 0.0107/0.1488

= 0.0719