Final answer:
To solve this probability problem, we can use the formula for probability of independent events. For part (a), the probability of selecting all five brand A bottles is (9/16) * (8/15) * (7/14) * (6/13) * (5/12). For part (b), the probability of selecting exactly two brand A bottles is (9/16) * (8/15) * (7/14) * (7/13) * (6/12) * (5/11) * 5C2. For part (c), the probability of selecting none of the brand A bottles is (7/16) * (6/15) * (5/14) * (4/13) * (3/12).
Step-by-step explanation:
To solve this problem, we can use the concept of probability. Let's go through each part of the question:
(a) To calculate the probability that all five bottles are brand A, we need to consider that there are 9 bottles of brand A and a total of 16 bottles. We can use the formula for probability of independent events, which is the number of favorable outcomes divided by the number of possible outcomes. So, the probability would be (9/16) * (8/15) * (7/14) * (6/13) * (5/12).
(b) To calculate the probability that exactly two bottles are brand A, we need to consider that there are 9 bottles of brand A and a total of 16 bottles. We can use the combination formula to calculate the number of ways to choose 2 bottles out of 5 and then multiply it by the probability of selecting brand A bottles and brand B bottles. So, the probability would be (9/16) * (8/15) * (7/14) * (7/13) * (6/12) * (5/11) * 5C2.
(c) To calculate the probability that none of the bottles are brand A, we need to consider that there are 9 bottles of brand A and a total of 16 bottles. We can use the formula for probability of independent events, which is the number of favorable outcomes divided by the number of possible outcomes. So, the probability would be (7/16) * (6/15) * (5/14) * (4/13) * (3/12).