Question

If 10% of a group ate sandwiches two days in a row, and 40% of the group had a sandwich on the first day, this means that 25% of the group that ate a first sandwich had a second. A. True B. False

Answer 1

The problem can be represented on a Venn diagram, as shown below.

We have P(Day 1 ∩ Day 2) = 0.1 and P(Day 1) = 0.4
We can deduce that 30% of the group ONLY had sandwiches on Day 1 and there's 60% of the group ONLY had sandwiches on Day 2.

We obtain the value 60% = 0.6 from 100%-(10%+30%)=60%

We also can deduce that there 70% of the group that had sandwiches on Day 2

The proportion of people who ate sandwiches on Day 2 GIVEN that they ate sandwiches on Day 1 is given by

P(Day 1 ∩ Day 2)÷P(Day 2) = 0.1÷0.4 = 0.25 = 25%

The statement is TRUE