Assume there are $400$ athletes in a training camp, who are required to attend the morning drill starting at $4$ am. The attendance in morning drills is $70\%$, i.e. on an average, $280$ athletes are present. Fifty new athletes are admitted in this batch.
What is the probability of attendance being at least $70\%$ among the new athletes, thus ensuring the overall attendance does not fall below $70\%$?
The training coach thinks that this probability will increase if the new batch size is $40$ instead of $50$. Is he assuming right?
I tried solving the first part by following method.
Let New athlete = N.A, Old athlete = O.A.
probability of N.A = $(50 / 400 ) = 1 / 8$.
probability of O.A = $(350 / 400 ) = 7 / 8$.
Then according to the question the ans should be $0.7*(0.125) + 0.8*(0.125) + 0.9*(0.125) + 1*(0.125)$ which is $0.425$. But I am not sure of this answer.