I am self studying, and have the answer to this question at the back of the book. The question is as follows (paraphrase): A survey of chemical research workers has shown on average that each man requires no cupboard 60% of the time, one cupboard 30% of the time and two cupboards 10% of the time; three or more were never needed. If four chemists work independently, how many cupboards should be provided so that there are adequate facilities at least 95% of the time? The answer is that 4 cupboards are enough for 95.85% of the time. I just do not know how to get the answer.

Jared Lowe

Jared Lowe

Answered question

2022-11-10

I am self studying, and have the answer to this question at the back of the book. The question is as follows (paraphrase):
A survey of chemical research workers has shown on average that each man requires no cupboard 60% of the time, one cupboard 30% of the time and two cupboards 10% of the time; three or more were never needed. If four chemists work independently, how many cupboards should be provided so that there are adequate facilities at least 95% of the time?
The answer is that 4 cupboards are enough for 95.85% of the time. I just do not know how to get the answer.

Answer & Explanation

postotnojeyf

postotnojeyf

Beginner2022-11-11Added 16 answers

Let a be the time when a person needs no cupboard, b when he needs 1, and c when he needs 2. These are the possible situations when there is enough cupboard space:
a a a a b a a a a b a a a a b a a a a b b b a a b a b a b a a b a b b a a b a b a a b b c a a a a c a a a a c a a a a c
Then we simply add the probabilities of each of these situations happening:
[ 60 % 60 % 60 % 60 % ] + 4 [ 60 % 60 % 60 % 30 % ] + 6 [ 60 % 60 % 30 % 30 % ] + 4 [ 60 % 60 % 60 % 10 % ]
which comes out to be 95.85%.

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