... heads and tails) and John 2n;jointly 22n+1outcomes that are equally likely. Let HM and TMbe the number of Mary’sheads and tails and HJ and TJJohn’s, then HM+ TM= n + 1 and HJ+ ... independent, (ii) A2 and B are independent, and (iii) A1 and A2are disjoint, then A1∪A2 and B are independent. If (i) and (ii) hold and A1⊂A2then B and A2\A1are also independent.Intuitively, ... An= nth toss is a head, with An = p and Probability and Statistics by Example: I Probability and statistics are as much about intuition and problem solving, asthey are about theorem...