Would it be rational for an agent to hold the three beliefs
$P(A) {0.4}$, $P(B) {0.3}$, and
$P(A \lor B) {0.5}$? If so, what range of probabilities would
be rational for the agent to hold for $A \land B$? Make up a table like
the one in Figure de-finetti-table, and show how it
supports your argument about rationality. Then draw another version of
the table where $P(A \lor B)
{0.7}$. 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. (*Hint:* what is Agent 1 committed to about the
probability of each of the four cases, especially the case that is a
loss?)

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