In: Advanced Math
James Bond, Q, and M have agreed to meet at a pub after work for drinks. Bond cannot remember if they agreed to meet at the “Fanny on the Hill” or at “My Father’s Moustache” - so he tosses a coin to decide which pub to go to. Q is also in the same predicament; he tosses a coin to decide between “My Father’s Moustache” and “The Quiet Woman”. M faced with same quandary flips a coin first to decide whether or not he needs to head to the “Fanny on the Hill”. If the answer is “no”, then he flips again to decide between “My Father’s Moustache” and “The Quiet Woman”. What is the probability that
(a) Bond and Q meet? (b) Q and M meet? (c) all three meet? (d) all three go to different places? (e) at least two meet?