An analyst has established the following prior probabilities regarding a company's next quarter's earnings per share (EPS) exceeding, equaling, or being below the consensus estimate.
Prior Probabilities
EPS exceed consensus
25%
EPS equal consensus
55%
EPS are less than consensus
20%
Several days before releasing its earnings statement, the company announces a cut in its dividend. Given this new information, the analyst revises his opinion regarding the likelihood that the company will have EPS below the consensus estimate. He estimates the likelihood the company will cut the dividend, given that EPS exceeds/meets/falls below consensus, as reported below.
Probabilities the Company Cuts Dividends, Conditional on EPS Exceeding/Equaling/Falling below Consensus
P(Cut div│EPS exceed)
5%
P(Cut div│EPS equal)
10%
P(Cut div│EPS below)
85%
The analyst thus determines that the unconditional probability for a cut in the dividend, P(Cut div), is equal to 23.75%. Using Bayes’ formula, the updated (posterior) probability that the company’s EPS are below the consensus is closest to:
A 85%.
B 72%.
C 20%.
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