Numbers 1 to 20 are placed in a bag. Without replacing the first number, what is the probability that the first number drawn will be odd and the second one will be even?

1 answer

When we take the first number out of the bag, there are 20 numbers and 10 of them are odd. So, the probability of drawing an odd number is 10/20 or 1/2.

Since the first number is not replaced, there will be 19 numbers left in the bag, including 9 even numbers. Thus, the probability of drawing an even number after drawing an odd number on the first draw is 9/19.

The probability of these two events happening together is the product of their probabilities:

P(Odd on first draw) * P(Even on second draw | Odd on first draw)

= (10/20) * (9/19)

= 9/38

Therefore, the probability of drawing an odd number on the first draw and an even number on the second draw is 9/38.