The numbers don't add up in this Venn diagram?

Question

I'm trying to draw a Venn diagram to make sense of the overlapping 3 pairs of brightly colored and stripped socks but the numbers don't add up to the 10 pairs given in the question? How can there be 10 pairs of socks?

Answer 1

(https://i.stack.imgur.com/5JfCJ.jpg)

I copied your diagram and added. The universe U for the Venn diagram is the total socks (which is 10). There is part in the venn diagram which is neither brightly colored or striped (denoted by A in the venn diagram). In this case, to calculate A, the total socks is 10 so
$$A + 1 + 3 + 3 = 10$$ $$A = 3$$ So, the probability to wear colored or striped socks in first day is $$\frac{1+3+3}{10}=\frac{7}{10}$$ Assuming I wear colored or striped socks in first day, the probability of wearing colored or striped socks in second day is $$\frac{1+3+3-1}{10-1}=\frac{6}{9}$$ Assuming I wear colored or striped socks in first and second day, the probability of wearing colored or striped socks in thirdday is $$\frac{1+3+3-2}{10-2}=\frac{5}{8}$$ So, the answer is
$$\frac{7}{10}*\frac{6}{9}*\frac{5}{8}$$

Answer 2

There can also be socks that are neither brightly colored nor striped.

Answer 3

You are correct - the numbers do not add up. If we have 10 pairs and 6 brightly coloured and 4 striped - this immediately implies that there can be none with both characteristics.