Find the probability that a randomly taken two-digit number will be a multiple of either 4 or 5, or both at the same time.

There are 90 two-digit numbers (from 10 to 99). This is the total number of outcomes when choosing a two-digit number.
Let A be an event such that the chosen number at random is a multiple of 5. There are 18 such two-digit numbers.
B – an event such that a randomly chosen number is a multiple of 4. There are 22 such two-digit numbers.
Numbers that are simultaneously multiples of 4 and 5 are four.
Then P (A) = 18/90; P (B) = 22/90;
The probability that the number is simultaneously a multiple of 4 and 5:
P (AB) = 4/90;
By the addition theorem for joint events, we get:
P (A + B) = P (A) + P (B) – P (AB) = 18/90 + 22/90 – 4/90 = 36/90 = 4/10 = 0.4.
Answer: The probability is 0.4.