3.20 Existing records reveal the following information about events A and B, where A = a long March warm spell and B = an April flood.
Year 1 2 3 4 5 6 7 8 9 10
A = warm March? No No Yes No Yes No Yes No Yes No
B = April flood? Yes No No Yes Yes Yes No Yes Yes No
On the basis of this 10-yr record, answer the following:
a) Are variables A and B independent? Prove.
b) Are variables A and B mutually exclusive? Prove.
c) Determine the marginal probability of an April flood.