Question

Alice and Bob share a bank account which contains an a priori unknown total amount of money T, Whenever Alice goes to the cash machine, the available amount for withdrawal A for Alice is always 10 Of the total T . Similarly, when Bob goes to the cash machine the available amount for withdrawal B for Bob is 10 Of the total T, Whatever the amount in the bank, Alice and Bob check their available amounts for withdrawal independently,

Draw a belief network that expresses this situation and show that A B.

Answer 1

A belief network can be used to represent the situation where Alice and Bob share a bank account, with nodes for the available amounts for withdrawal and the total amount of money. The probabilities of the available amounts being equal to 10% of the total amount are both 1, showing that A and B are equal.

Step-by-step explanation:

To represent the situation where Alice and Bob share a bank account, we can create a belief network. In this network, we have two nodes: A and B, representing the available amounts for withdrawal for Alice and Bob, respectively. We also have a node T, representing the total amount of money in the bank account. The probability of A being equal to 10% of T is 1, as Alice always withdraws 10% of the total amount. Similarly, the probability of B being equal to 10% of T is also 1.

To show that A and B are equal, we can calculate their probabilities individually. Since A is always 10% of T, the probability of A being equal to B is 1. Therefore, A and B are equal.