# Question

Would it he rational for an agent to hold the three beliefs P (A) = 0.4, P (B) = 0.3, and P (A V B) = 0.5? If so, what range of probabilities would be rational for the agent to hold for A ^ B. Make tip a table like the one in Figure, and show how it supports your argument about rationality. Then draw another version of the table where P (A V B) = 0.7. Explain why it is rational to have this probability, even though the table shows one case that is a loss and three that just break even.

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