Complete a Venn diagram, calculate conditional probability and sample a group without replacement.

In a school of 88 boys, 32 study economics (E), 28 study history (H) and 39 do not study either subject. This information is represented in the following Venn diagram. U E H a b c 39

1. Calculate the values a, b, c.[4]
2. A student is selected at random.[3]
   1. Calculate the probability that he studies both economics and history.
   2. Given that he studies economics, calculate the probability that he does not study history.
3. A group of three students is selected at random from the school.[5]
   1. Calculate the probability that none of these students studies economics.
   2. Calculate the probability that at least one of these students studies economics.