Question: A mathematics professor, when leaving for work, forgets his car keys with a probability p1 and his office keys with a probability p2 (we assume

A mathematics professor, when leaving for work, forgets his car keys with a probability p1 and his office keys with a probability p2 (we assume that these two events are independent).

(i) What is the probability that during a week (i.e. in five working days) there will be at least one day when he forgets both sets of keys?

(ii) What is the probability that in exactly three days he will forget at least one set of keys?

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