Make a table: | blue | red | --------|------|------|----- pearls | | | --------|------|------|----- empty | |

Make a table: | blue | red | --------|------|------|----- pearls | | | --------|------|------|----- empty | | | --------|------|------|----- | | | 100 We know that 40% of the eggs are blue, so we fill in 40 at the bottom row in the blue column. We now also know that 60% are red. Similarly, 20% of eggs are empty & red, so we fill in 20 there. Now we can calculate that 60% - 20% = 40% are pearls & red: | blue | red | --------|------|------|----- pearls | | 40 | --------|------|------|----- empty | | 20 | --------|------|------|----- | 40 | 60 | 100 Now comes the final bit of data: 5/13 of the eggs containing pearls are painted blue: | blue | red | --------|------|------|----- pearls | X | 40 | 40+X --------|------|------|----- empty | | 20 | --------|------|------|----- | 40 | 60 | 100 With X = 5/13*(40+X), or X = 100/3. | blue | red | --------|-------|------|----- pearls | 100/3 | 40 | 220/3 --------|-------|------|----- empty | 20/3 | 20 | 80/3 --------|-------|------|----- | 40 | 60 | 100 Now we can answer the question: what is the probability that an egg painted blue contains a pearl? For every 40 blue eggs, 100/3 contain pearls. So the answer is 100/3/40 = 5/6.