A box contains 70 marbles, each of them purple, pink or blue. If a marble is picked at random, the probability that it is purple is \(\frac{3}{7}\) and the probability that it is either purple or pink is \(\frac{4}{7}\). How many pink marbles are there in the box?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 10
Every marble is equally likely to be picked, so number of marbles of a kind = probability × total. A marble is either purple or pink in as many ways as there are purple and pink marbles together.
Purple marbles \(\displaystyle =\frac{3}{7}\times70=30\)
Purple and pink marbles together \(\displaystyle =\frac{4}{7}\times70=40\)
Pink marbles \(=40-30=10\)