Question

suppose i place 2 red balls, 3 green balls, and 4 blue balls into a hat, and draw two balls without replacement. what is the probability they are both blue?

Answer 1

The probability of drawing two blue balls without replacement is \( \frac{4}{9} \times \frac{3}{8} = \frac{1}{6} \).

Step-by-step explanation:

To find the probability of drawing two blue balls without replacement, we start by calculating the probability of drawing a blue ball on the first draw. Initially, there are 4 blue balls out of a total of 9 balls (2 red + 3 green + 4 blue), giving us a probability of \( \frac{4}{9} \) to draw a blue ball on the first attempt.

Once a blue ball has been drawn, there are now 8 balls left in the hat (since one blue ball has been removed), with 3 blue balls remaining out of these 8. Therefore, the probability of drawing another blue ball on the second attempt is \( \frac{3}{8} \).

To find the overall probability of drawing two blue balls consecutively, we multiply the probability of the first draw (\( \frac{4}{9} \)) by the probability of the second draw (\( \frac{3}{8} \)). This multiplication gives us \( \frac{4}{9} \times \frac{3}{8} = \frac{1}{6} \), which represents the probability of drawing two blue balls consecutively without replacement from the hat containing 2 red, 3 green, and 4 blue balls.

Answer 2

Step-by-step explanation:

we are given 2 red balls, 3 green balls and 4 blue balls for a total of 9 balls in the hat. we are to take two balls and find the probability that both are blue.

the first probability would be

`(4)/(9)`

as probability is equal to (number of favorable outcomes) / number of total outcomes). so we have 9 total outcomes and 4 favorable ones (4 balls we want)

next, we have remaining 2 red balls, 3 green balls, 3 blue balls and 8 total balls. again, the second probability is

`(3)/(8)`

we have 8 total outcomes and 3 favorable ones (3 blue balls we want).

thus, their product is our total probability.

`(4)/(9) * (3)/(8) \\ = (12)/(72) \\ = (1)/(6)`

thus, our probability is 1/6.