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?
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.
To calculate the probability of drawing an odd number as the first draw and an even number as the second draw without replacement, we need to determine the total number of outcomes and the desired outcomes.
Total Number of Outcomes:
There are 20 numbers in the bag initially.
Desired Outcomes:
The first number should be odd, which means there are 10 odd numbers (1, 3, 5, 7, 9, 11, 13, 15, 17, and 19).
After the first number is drawn, there are 19 numbers left in the bag. To have the second number drawn be even, there are 10 even numbers to choose from (2, 4, 6, 8, 10, 12, 14, 16, 18, and 20).
Calculating the Probability:
The probability is calculated by dividing the number of desired outcomes by the total number of outcomes.
Probability = (Number of desired outcomes) / (Total number of outcomes)
In this case, the number of desired outcomes is 10 (odd numbers) * 10 (even numbers) = 100.
Therefore, the probability is 100 / (20 * 19) = 100 / 380 = 1 / 3.8 = 0.263, or approximately 26.3%.
So, there is a 26.3% probability of drawing an odd number as the first draw and an even number as the second draw without replacement from the bag.
To find the probability, we need to determine the total number of outcomes and the number of desired outcomes.
Total Number of Outcomes:
We have 20 numbers to choose from, so the total number of outcomes is 20.
Number of Desired Outcomes:
First, we need to select an odd number from the bag. There are 10 odd numbers between 1 and 20 (1, 3, 5, 7, 9, 11, 13, 15, 17, 19). Once an odd number is chosen, there are 19 numbers left in the bag for the second selection. Out of these, 10 are even numbers (2, 4, 6, 8, 10, 12, 14, 16, 18, 20).
Therefore, the number of desired outcomes is 10 for the first number multiplied by 10 for the second number, giving us 10 * 10 = 100.
Probability Formula:
Probability = Number of Desired Outcomes / Total Number of Outcomes
Probability = 100 / 20
Probability = 5/1 or 1/2
So, the probability that the first number drawn will be odd and the second one will be even without replacing the first number is 1/2 or 50%.