An overnight shipment contains 2 bottles of Aspirin and 3 bottles of thyroid tab

Question

An overnight shipment contains 2 bottles of Aspirin and 3 bottles of thyroid tablets. A second shipment contains 3 bottle of aspirin, 2 bottles of thyroid and 1 bottle of laxative tablets. If one bottle is randomly chosen from each of the two shipments, find the following:
a) p(Both bottles contain tablets for thyroid)?
b)P(Neither bottle contains thyroid tablets)?
c)P(Both bottles contain aspirin tablets given that at least one bottle contains aspirin tablets)?
d)P(One bottle contains aspirin and another bottle contains thyroid tablets)?

Explanation / Answer

Overnite case: 2A+3T=5bottles
Tote bag: 3A+2T+1L=6bottles
.
Both are T: 3/5 * 2/6 = 6/30 = 1/5
.
Neither are T: 2/5 * 4/6 = 8/30 = 4/15


.
Different Tablets:
A and non A: 2/5 * 3/6 = 6/30 = 1/5
T and non T: 3/5 * 4/6 = 12/30 = 2/5
1/5 + 2/5 = 3/5 Ans.

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