Question: A box contained 1,500 marbles of which 600 were red and the others were blue. The following procedure was repeated many times:
One hundred draws were made at random with replacement from the box; the number of red marbles among the draws was counted.
The first 10 counts were all smaller than 40. Compute the approximate probability for this event.  Edit

Answer: This is an binomial experiment
In binomial experiment we know,
P(x=i) = nCi p^i q^(n - i)

Here, n = 100, p = 0.4, q = 1 - p = 0.6

The probability that less than 40 out of 100 draws means P(x < 50) =P(x=0)+P(x=1)+....+P(x=39)
=(100C0*0.4^0*0.6^100)+(100C1*0.4^1*0.…
=0.462

So, for the first 10 counts were all smaller than 40 it will be (0.462)^10
= 0.000443016351 (Ans.)  Edit