Question

Handshaking party! Five doctors attend a meeting. Call them D1, D2, D3, D4, D5. Each pair of doctors has an independent, 50% chance of shaking hands with each other. E.g. {12, 15, 24, 34} could represent one outcome, in which D1 shakes hands with D2 and D5, and D2 and D3 each shake hands with D4. This would be the same as {42, 15, 21, 34}: it doesn't matter what order we list handshakes in, and handshakes are symmetric. Let Xk denote the number of people that Dk shakes hands with, for k = 1, 2, 3, 4, 5. So, in the example above, we would have X1 = X2 = X4 = 2 and X3 = X5 = 1. What is the highest possible total number of handshakes? How big is the sample space for this experiment? 3. What is the expected total number of handshakes that take place? 4. Calculate P {X1 = 2} ∩ {X2 = 2}. (Hint: This is a delicate problem. You probably need to handle it case-by-case.) 5. Calculate the conditional probability P {X1 = 2} | {X2 = 2}.

          Handshaking party! Five doctors attend a meeting. Call them D1, D2, D3, D4, D5. Each pair of doctors has an independent, 50% chance of shaking hands with each other. E.g. {12, 15, 24, 34} could represent one outcome, in which D1 shakes hands with D2 and D5, and D2 and D3 each shake hands with D4. This would be the same as {42, 15, 21, 34}: it doesn't matter what order we list handshakes in, and handshakes are symmetric. Let Xk denote the number of people that Dk shakes hands with, for k = 1, 2, 3, 4, 5. So, in the example above, we would have X1 = X2 = X4 = 2 and X3 = X5 = 1.
What is the highest possible total number of handshakes?
How big is the sample space for this experiment?
3. What is the expected total number of handshakes that take place?
4. Calculate P {X1 = 2} ∩ {X2 = 2}. (Hint: This is a delicate problem. You probably need to handle it case-by-case.)
5. Calculate the conditional probability P {X1 = 2} | {X2 = 2}.

Added by Kelly B.

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