Just when I got the hang of probability, I get this question and I'm so lost. Can anyone help?
Molly has a jar containing 4 yellow, 3 blue, 3 green, and two orange marbles.
Molly returned all marbles to the jar. She then removed some marbles of one color from the jar. The removal changed the probability of drawing that color marble in 1 turn to equal 1/5. Name the color and number of marbles Molly removed.
A) 2 orange
B) 2 blue
C) 2 yellow
D) 2 green
There are twelve
remove two and we have ten
two orange = now we have no orange
two blue = now we have 1 blue so 1/10
two yellow = now we have 2 yellow so 2/10 = 1/5
two green = now we have no green
Here's an example of what the question is asking for:
If Molly removed 2 orange marbles, the probability of drawing an orange marble from the remaining batch is
P(Orange) = (2-2)/(4+3+3+0) = 0/10 = 0
and that does not equal 1/5, so she did not remove 2 orange marbles.
Since in all cases, two marbles have been removed, leaving 10 marbles, and
P(colour?)=1/5
So the remaining coloured marble is
10*(1/5)=2
What coloured marble will have two left after removing 2 of that colour?
Thank you!!!!!! I get it now.
To solve this problem, we need to understand the concept of probability and how it relates to the given information.
First, let's calculate the original probability of drawing a particular color marble from the jar in one turn.
The total number of marbles in the jar is 4 (yellow) + 3 (blue) + 3 (green) + 2 (orange) = 12 marbles.
The probability of drawing a yellow marble in one turn is 4 (yellow marbles) / 12 (total marbles) = 1/3.
Since Molly removed some marbles of one color from the jar, the total number of marbles in the jar has changed. Now, we need to find the new probability of drawing that color marble in one turn, which is equal to 1/5.
Let's consider the options provided:
A) If Molly removed 2 orange marbles from the jar, the total number of marbles in the jar would become 12 (original total) - 2 (removed orange marbles) = 10 marbles. The probability of drawing an orange marble would be 2 (orange marbles) / 10 (total marbles) = 1/5. So, this option is a possible answer.
B) If Molly removed 2 blue marbles from the jar, the total number of marbles in the jar would become 12 (original total) - 2 (removed blue marbles) = 10 marbles. The probability of drawing a blue marble would be 3 (blue marbles) / 10 (total marbles) = 3/10, which is not equal to 1/5. So, this option is not the correct answer.
C) If Molly removed 2 yellow marbles from the jar, the total number of marbles in the jar would become 12 (original total) - 2 (removed yellow marbles) = 10 marbles. The probability of drawing a yellow marble would be 4 (yellow marbles) / 10 (total marbles) = 2/5, which is not equal to 1/5. So, this option is not the correct answer.
D) If Molly removed 2 green marbles from the jar, the total number of marbles in the jar would become 12 (original total) - 2 (removed green marbles) = 10 marbles. The probability of drawing a green marble would be 3 (green marbles) / 10 (total marbles) = 3/10, which is not equal to 1/5. So, this option is not the correct answer.
Therefore, the correct answer is option A) 2 orange marbles, as removing these marbles would change the probability of drawing an orange marble in one turn to 1/5.