SOLUTION: jar contains 110 marbles of which 50 are red and 60 are green. The probability of picking a red marble from the jar without looking is, therefore, 50/110. How many red marbles mu

Algebra ->  Probability-and-statistics -> SOLUTION: jar contains 110 marbles of which 50 are red and 60 are green. The probability of picking a red marble from the jar without looking is, therefore, 50/110. How many red marbles mu      Log On


   

Question 307073: jar contains 110 marbles of which 50 are red and 60 are green. The probability of picking a red marble from the jar without looking is, therefore, 50/110. How many red marbles must be added to the jar so that the probability of picking a red marble will be 2/3?
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
If you add x red marbles to the jar, then there will be
50+x red marbles, and 110 + x total marbles. If the final probability is to be 2/3, then solve this equation:

%2850%2Bx%29%2F%28110%2Bx%29+=+2%2F3

Since a%2Fb=c%2Fd+ means that ad=bc,
%2850%2Bx%29%2F%28110%2Bx%29=2%2F3 means that 3%2850%2Bx%29=2%28110%2Bx%29
150+%2B+3x=220%2B+2x

Subtract 2x from each side:
150%2Bx=+220

Subtract 150 from each side:
x=+70

Check: You now have 50+70=120 red marbles, and 110 + 70= 180 total marbles.
The probability of getting a red marble is 120%2F180=2%2F3.

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus