Question 637500: A jar contains 24 red and blue marbles. If the probability of selecting a red marble at random is 3/8, then how many red marbles must be added so that the probability of randomly selecting a red marble becomes 1/2 ?
(1) 3/8 = x/24
3[24]= 8x
72 = 8x
9 = x
(2) 9 red marbles
24-9 = 15 blue marbles
(3) 15-9 = 6 more red marbles
(4) [9+6]/[24+6]= 15/30 = 1/2
On step 3 I did not really know what to do so I just guessed and played with
numbers. I finally arrived at an answer when I subtracted the red marbles from the blue marbles, but I do not understand why this works.Guessing,checking,and luck will take a long time on an exam. How do I solve these type of problems? For example what would I do if I needed to find how many more red marbles are needed to go from a probability of 3/8 to 209/698? Please explain.
PS: What concepts do I need to review or learn in order to work problems like this or more difficult ones in this area?
I am sorry this is so long, but I would sincerely appreciate your time and effort with my dilemma.
- disgruntled student(Konny)
Answer by DrBeeee(684)   (Show Source):
You can put this solution on YOUR website! This may help your step 3.
Let x = number of red marbles to add to get 50%
You correctly calculated that there are 9 red marbles in the jar. The jar contains a total of 24 marbles is a given.
You want add x red marbles to the 9 to end up with (9+x) which is 50% or 1/2 the total number, which is now (24 + x) because you also add x to the total.
This results in the same ratio that you have, except you deduced that x = 6. That is you now have the algebraic equation
(9+x)/(24+x) = 1/2
Using cross multiplication we get
2*(9+x) = (24+x) or
18 + 2x = 24 + x
x = 24 - 18
x = 6
Answer: You need to add 6 red marbles.
Now you can rely on your math skill. However, don't toss out your super deductive reasoning.
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