An urn contains 8black and
7 green balls. Five balls are randomly drawn from the urn in succession, with replacement. That is, after each draw, the selected ball is returned to the urn. What is the probability that all
5balls drawn from the urn are green? Round your answer to three decimal places.
Why did the green ball go to the party?
Because it wanted to have a ball of a time!
Now, let's calculate the probability of drawing all 5 green balls from the urn.
There are a total of 15 balls (8 black and 7 green) in the urn. Since we are drawing with replacement, the probability of drawing a green ball on each attempt is 7/15.
The probability of drawing all 5 green balls can be calculated by multiplying the probabilities of each individual draw:
(7/15) * (7/15) * (7/15) * (7/15) * (7/15)
Calculating this expression gives us a probability of approximately 0.079, rounded to three decimal places.
So, the probability of drawing all 5 green balls from the urn is approximately 0.079.
To find the probability of drawing all 5 green balls, we need to calculate the probability of drawing one green ball and then multiply it by itself for each successive draw.
The probability of drawing one green ball is:
P(Green) = Number of green balls / Total number of balls
P(Green) = 7 / (7+8)
P(Green) = 7 / 15
Since replacement is allowed, the probability of drawing a green ball in each of the 5 successive draws is the same.
Thus, the probability of drawing all 5 green balls is:
P(5 Green balls) = (P(Green))^5
P(5 Green balls) = (7/15)^5
Using a calculator, we find:
P(5 Green balls) = 0.063
Therefore, the probability that all 5 balls drawn from the urn are green is 0.063, rounded to three decimal places.
To find the probability that all 5 balls drawn from the urn are green, we need to calculate the probability of drawing a green ball in each of the 5 successive draws and then multiply them together.
The probability of drawing a green ball in one draw is given by the ratio of the number of green balls to the total number of balls in the urn. In this case, there are 7 green balls and a total of 8 black balls + 7 green balls = 15 balls.
So, the probability of drawing a green ball in one draw is 7/15.
Since the balls are replaced after each draw, the probability of drawing a green ball in each of the 5 successive draws is the same: 7/15.
To find the probability of all 5 draws being green, we multiply these probabilities together:
(7/15) * (7/15) * (7/15) * (7/15) * (7/15) = 16807/759375 ≈ 0.022
Rounding to three decimal places, the probability is approximately 0.022.
8 black and 7 green in urn (15 in all)
5 drawn with replacement.
Probability that first one is green:
P(1)=7/15
Probability that second one is green
P(2)=7/15
(ball is replaced)
...
P(5)=7/15
For all 5 steps to succeed, multiply together the individual probabilities
P(all five are green)
=(7/15)*(7/15)*(7/15)*(7/15)*(7/15)
=(7/15)^5
I will leave you to do the calculator part to evaluate to three decimal places.