Question

There is a bag with only red marbles and blue marbles. The probability of randomly choosing a red marble is 2 9 . There are 63 marbles in total in the bag and each is equally likely to be chosen. Work out how many red marbles there must be.

Answer 1

The main idea is the number of marbles and the denominator of the probability. All you have to do is multiply the fraction by a fraction which is equal to 1 which makes the denominator equal to 63. We know 63 is a multiple of 9. 9 goes 7 times in 63 so we multiple the fraction $\frac{2}{9}$ with $\frac{7}{7}$ which gives, $\frac{2 * 7}{9 * 7}$ which when evaluated gives $\frac{14}{63}$ and the numerator is the number of red marbles in the bag. So there are 14 red marbles in the bag :D