The events A, B, and C occur with respective probabilities 0.08, 0.47, and 0.23. The events A and B are mutually exclusive; likewise the events A and C are mutually exclusive. The probability of the event ∩BC is 0.16. Compute the probability of the event ∪B∩CA.

Acompany manufactures three types of cabinets. it makes 110 cabinets each week. in the first week, the sum of the number of type-1 cabinets and twice the number of type-2 cabinets produced was 10 more than the number of type-3 cabinets produced. the next week, the number of type-1 cabinets produced was three times more than in the first week, no type-2 cabinets were produced, and the number of type-3 cabinets produced was the same as in the previous week.