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A researcher estimates that the probabilities of share C and D increasing are 61% and 75%...

A researcher estimates that the probabilities of share C and D increasing are 61% and 75% respectively.

The event that share C increases is denoted by C, and the event that share D increases is denoted by D.

Assume that share can increase or decrease only.

(1) If events C and D are independent, what is the probability that both shares increase?

(2) Show that the probability of both shares increasing cannot be less than 36%, no matter whether events C and D are independent or not.

(3) Assume it is impossible for both shares to decrease, what is the probability that both shares increase?

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