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 the 10-year 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.
(d) Determine the probability of having a cold March next year.
(e) Determine the probability (one value) of having both a cold March and a flood-free April next year.
(f) If a long March warm spell has just ended today, what is the best estimate of the probability of a flood in April?
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