The urn contains 5 and 3 black balls. 5 balls are taken out of the urn at once. Find the probability that 4 of them will be white?

A big event consists of two small independent ones, here is its formula:
P (C) = P (A) * P (B)

Big event – 4 out of 5 balls will be white
Substitute in the formula and get:
P (C) = first ball is white and second ball is white and 3 is white and 4 is white and 5 is ball is black
And- multiplication
We get:
P (C) = P (b) * P (b) * P (b) * P (b) * P (h)

To find a small event:
P (A) = favorable outcomes (m) / number of total outcomes (n)

There are 8 outcomes in total, because 5 white and 3 black – add them up and get 8.
P (b) = 5/8 = 0.6 (5 because we have 5 white balls, these are favorable for us)
P (h) = 3/8 = 0.4 similarly

Now we substitute in our formula:

P (C) = 0.6 * 0.6 * 0.6 * 0.6 * 0.4 = 0.052