There are 2 white and 8 black balls in the basket. 2 balls are taken out of the basket in succession, after taking out

There are 2 white and 8 black balls in the basket. 2 balls are taken out of the basket in succession, after taking out the first one it is returned to the basket. Find the probability that 1) both balls are white; 2) colored balls are taken out

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

1. Big event – both balls will be white.
Substitute in the formula and get:
P (C) = white and white
And- multiplication
We get:
P (C) = P (b) * P (b)

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

There are 10 outcomes in total, because 2 white and 8 black
P (b) = 2/10 = 0.2 (2 because 2 white balls, these are favorable for us)

Now we substitute in our formula:
P (C) = 0.2 * 0.2 = 0.04

2. Big event – colored balls are taken out, i.e. White and black.
Substitute in the formula and get:
P (C) = white and black
And- multiplication
We get:
P (C) = P (b) * P (h)

P (b) we found = 0.2
P (h) = 8/10 = 0.8 (8 because 8 black balls, these are favorable for us)

Now we substitute in our formula:
P (C) = 0.2 * 0.8 = 0.16