Expand Your Knowledge: Conditional Probability In the western United States, there are many dry-land wheat farms that depend on winter snow and spring rain to produce good crops. About 65% of the years, there is enough moisture to produce a good wheat crop, depending on the region (Reference: Agricultural Statistics, U.S. Department of Agriculture).

(a) Let r be a random variable that represents the number of good wheat crops in n 5 8 years. Suppose the Zimmer farm has reason to believe that at least 4 out of 8 years will be good. However, they need at least 6 good years out of 8 to survive financially.

Compute the probability that the Zimmers will get at least 6 good years out of 8, given what they believe is true; that is, compute P(6 # r | 4 # r).

(b) Let r be a random variable that represents the number of good wheat crops in n 510 years.

Suppose the Montoya farm has reason to believe that at least 6 out of 10 years will be good.

However, they need at least 8 good years out of 10 to survive financially. Compute the probability that the Montoyas will get at least 8 good years out of 10, given what they believe is true; that is, compute P(8 # r | 6 # r).

(c) List at least three other areas besides agriculture to which you think conditional binomial probabilities can be applied.

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