Marble Madness
Mrs. Fairbarn has a bag that contains exactly 3
black marbles, 6 gold marbles, 2 purple marbles and 6 red marbles.
Mrs. Fairbarn finds a number of white marbles and
adds them to the bag. She tells Mr. Huang that if he now draws (takes) a marble at
random from the bag, the probability of it being black or gold is 3/7.
How many white marbles did Mrs. Fairbarn add to the bag?
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ReplyDeletethank you, Krupa for sharing your answer =) I do need to ask you to check your final process since it may confuse a few people:
Delete- 7 times 3 =?
- 24 - 17 = ?
thanks
-Well since I multiplied the numerator by 3, you know how when you want to find equivalent fraction you multiply the denominator and the numerator by the same number, yeah so I multiplied the numerator, 3, by 3 I would have to do the same to the denominator, 7. So, 7 times 3 equals 21 which tells me 21 would now be the total number of marbles.
Delete-I think you mean 21-17 because I am subtracting the total amount of marbles (with white) subtracted by the previous total 17. This way my answer would be 4. So, Mrs. Fairbarn would have put 4 white marbles into the bag.
- I did 7 times 3 because because whenever you want to find the equivalent fraction you have to multiply the numerator by the same number you multiply the denominator and vice versa. So, since I multiplied the numerator by 3 I have to multiply the denominator by 3 as well.
Delete-I think you meant 21-17 because 21 is the total amount of marbles with the white ones and 17 is the total amount of marbles without the white ones. So, I subtracted it to find out how many white marbles Mrs. Fairbarn had added.
Hello.
ReplyDeleteTo solve this problem, I added the black and gold marbles together, and I got 9 marbles out of the total amount of marbles, 17. This is 9/17, which is not equivalent to 3/7. Since I know there will always be 9 black and gold marbles in the bag, I multiplied the numerator of 3/7, 3, by 3 to get 9. Since I multiplied the to[ by 3, I have to multiply the bottom by 3 as well. 7*3=21, therefore 3/7 is equivalent to 9/21. Coincidentally, there are also 9 black and gold marbles in the bag. To get to 3/7, there must be 21 marbles in the bag total, so I did 21-17=4, so she put 4 more marbles in the bag.
Good job and thank you for contributing.
DeleteOh hi.
ReplyDeleteI think the answer to this question is that Mrs. Faribarn added 4 white marbles to the bag. I came up with this answer by first adding all the given marble totals (3,6,2,6). The sum was 17. After identifying the total without white, I added 3 and 6. I choose these numbers because the probability of two marbles are the same. This means that black and gold are put as 'one group' and have the equal chance of getting picked. Key word: OR.
3+6=9. Chances of getting Black or Gold is 9 / ?. After this, I got 3/7 and multiplied it by 3 because I wanted the numerator to be the same as 9. 3x3=9. By conducting this method, I also identify the '?' because whatever you do to the numerator, you do to the denominator (vise-versa). 7x3=21. Therefore, the total is 21. I know I am correct because if I divide 9 / 21 by 3, I will find 3/7, which is the probability said in the question.
To find how many white marbles Mrs. Fairbarn added, I simply subtracted 21-17=4. Thus, 4 is how many marbles she added. 9 black and gold / 21 total marbles = 3 / 7 (simplified version).
Good job Johnathon. You did a good job explaning. However, I don't get where you got "Key word: OR.". Where did you get it???? There's no "or" in the paragraph.
ReplyDeleteThank you for your co-operation.
I got the 'no' from the sentence 'Black OR Gold'. I used this to understand what the question is asking me.
DeleteGreat work again folks. We really like seeing students asking and answering questions of each other. Make sure you also comment with some "Next Steps" for people to consider in the future. The official solution for the past week's POTW is below:
ReplyDeleteSolution:
In order to determine the probability that a marble drawn from the bag is black or gold, we
divide the number of black and gold marbles in the bag by the total number of marbles in the
bag. In other words,
Probability of selecting a black or gold marble =
Number of black or gold marbles/Total number of marbles
When she adds white marbles to the bag, this does not change the number of black or gold
marbles. Therefore, the number of black or gold marbles in the bag is 3 + 6 = 9.
We are also given that the probability of drawing a black or gold marble is
3/7
.
So the equation
Probability of selecting a black or gold marble = Number of black or gold marbles/Total number of marbles
becomes 3/7 = 9/Total number of marbles
Since
3/7 = 9/21, this tells us
9/21 = 9/Total number of marbles
Therefore, the total number of marbles is 21.
Originally, there were 3 + 6 + 2 + 6 = 17 marbles in the bag. Then Mrs. Fairbarn added some white
marbles. Since the total number of marbles in the bag after adding some white marbles is 21,
she must have added 21 - 17 = 4 white marbles.