Assume that you are drawing two balls without replacement from an urn that contains 13 green balls, 10 blue balls, and 1 red ball. What is the probability that you will draw a blue balls and a red ball?
prob(blue, then red)
= (10/24)(1/23)
= 5/276
Thanks Reiny.
To find the probability of drawing a blue ball and a red ball, we need to calculate the probability of drawing a blue ball first and the probability of drawing a red ball second.
Step 1: Find the probability of drawing a blue ball first.
There are a total of 13 green balls, 10 blue balls, and 1 red ball in the urn, so the total number of balls in the urn is 13 + 10 + 1 = 24.
The probability of drawing a blue ball first can be calculated as:
P(Blue ball) = (Number of blue balls)/(Total number of balls)
P(Blue ball) = 10/24
Step 2: Find the probability of drawing a red ball second.
After drawing a blue ball, there will be 9 blue balls left in the urn, along with 13 green balls. The total number of balls will be 9 + 13 = 22.
The probability of drawing a red ball second can be calculated as:
P(Red ball) = (Number of red balls)/(Total number of balls)
P(Red ball) = 1/22
Step 3: Combine the probabilities.
Since we are drawing the balls without replacement, the probability of drawing a blue ball and a red ball can be found by multiplying the probabilities of the two events together.
P(Blue ball and Red ball) = P(Blue ball) × P(Red ball)
P(Blue ball and Red ball) = (10/24) × (1/22)
Now, we can calculate the final probability:
P(Blue ball and Red ball) ≈ 0.0183 or 1.83%
To find the probability of drawing a blue ball and a red ball without replacement, we need to calculate the probability of each event separately and then multiply them together.
First, let's calculate the probability of drawing a blue ball. There are a total of 24 balls in the urn (13 green, 10 blue, and 1 red). When drawing the first ball, there are 10 blue balls out of a total of 24, so the probability of drawing a blue ball on the first draw is 10/24.
After the first ball is drawn, there are 23 balls left in the urn (since we didn't replace the first ball). Out of these, there is 1 red ball remaining. So the probability of drawing a red ball on the second draw, given that a blue ball was drawn on the first draw, is 1/23.
To find the probability of both events occurring, we multiply the probabilities together:
P(Blue ball and Red ball) = P(Blue ball) * P(Red ball | Blue ball)
= (10/24) * (1/23)
= 10/552
Therefore, the probability of drawing a blue ball and a red ball without replacement is 10/552.