Final answer:
The probability that the first number drawn will be odd is 1/2, and the second will be even is 5/19.
Step-by-step explanation:
The question asks about the probability of drawing an odd number first and an even number second from a bag containing numbers 1 to 20 without replacement.
To calculate this, we need to consider the sample space and the desired outcomes.
The sample space S is the whole numbers starting at one and less than 20 (1-19).
There are 10 odd numbers (1, 3, 5, 7, 9, 11, 13, 15, 17, 19) and 10 even numbers (2, 4, 6, 8, 10, 12, 14, 16, 18, 20).
The probability of drawing an odd number first is 10 out of 20, or 1/2.
After drawing an odd number, there are 19 numbers left, including 10 even numbers.
Therefore, the probability of then drawing an even number is 10 out of 19.
To find the combined probability of both events happening, we multiply the probabilities of each individual event:
P(odd first and even second) = P(odd first) × P(even second)
= 1/2 × 10/19
= 10/38, or simplified, 5/19.