suppose that a box contains 3 red and 2 green balls.rwo balls are drawn from tje box with out replacement.what is the probability that the first is red and the second is green
prob(red, then green) = (3/5)(2/4) = 3/10
To calculate the probability of drawing a red ball followed by a green ball, we need to consider the total number of possible outcomes and the number of favorable outcomes.
Step 1: Determine the number of balls in the box.
In this case, there are 3 red balls and 2 green balls, totaling 5 balls.
Step 2: Calculate the probability of drawing a red ball first.
Since there are 3 red balls in the box, the probability of drawing a red ball on the first draw is 3/5.
Step 3: Calculate the probability of drawing a green ball second.
After the first red ball is drawn, there will be 4 balls left in the box, with 2 green balls. Therefore, the probability of drawing a green ball on the second draw is 2/4.
Step 4: Multiply the probabilities.
To find the overall probability of drawing a red ball first and a green ball second, multiply the probabilities calculated in steps 2 and 3:
(3/5) * (2/4) = 6/20 = 3/10.
So, the probability that the first ball drawn is red and the second ball drawn is green is 3/10.
To find the probability that the first ball drawn is red and the second ball drawn is green, we need to calculate the probability of each event separately and then multiply them together.
Step 1: Calculate the probability of drawing a red ball first.
The total number of balls in the box is 3 red + 2 green = 5 balls.
Since the first ball is not replaced after it's drawn, there are now 4 balls left in the box, with only 2 of them being red.
Therefore, the probability of drawing a red ball first can be calculated as:
P(red first) = (number of red balls/total number of balls) = 3/5.
Step 2: Calculate the probability of drawing a green ball second.
After drawing a red ball, there are now 2 red balls and 2 green balls left.
Now, there are 4 balls in total, with 2 of them being green.
Therefore, the probability of drawing a green ball second can be calculated as:
P(green second) = (number of green balls/total number of balls) = 2/4.
Step 3: Multiply the probabilities from Step 1 and Step 2.
To find the probability of both events happening, we multiply their probabilities together:
P(first is red and second is green) = P(red first) * P(green second) = (3/5) * (2/4) = 6/20 = 3/10.
Therefore, the probability that the first ball drawn is red and the second ball drawn is green is 3/10.