Question

There is a bag with only red marbles and blue marbles. The probability of only choosing a red marble is 5/8. There are 25 red marbles in the bag and each is likely to be chosen. How many marbles should there be in total?

Answer 1

Answer: 40

25 red, 15 blue

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Work Shown:

b = number of blue marbles = unknown

r = number of red = 25

T = number total = 25+b

r/T = probability of getting red = 5/8

r/T = 5/8

25/(25+b) = 5/8

25*8 = 5(25+b) .... cross multiplication

200 = 125+5b

200-125 = 5b

75 = 5b

5b = 75

b = 75/5

b = 15

We have 15 blue marbles and 25 red marbles. This means there are T = r+b = 25+15 = 40 marbles total.

The proportion of red is r/T = 25/40 = (5*5)/(5*8) = 5/8 to help confirm we have the correct value for b.