Wiyot inspects a batch of products by sampling 4 of them without replacement. If at least one of the products is defective in the sample, the whole batch is sent back. Wiyot doesn't know it, but in the batch he is inspecting now, there are 100 products and 16 are defective. If he samples 4 products from this batch without replacement,what is the probability that... a) All of the products in the sample will be defective? b) None of the products in the sample are defective? c) At least one of the products is defective and the whole batch is sent back?
Wiyot inspects a batch of products by sampling 4 of them without replacement. If at least one of the products is defective in the sample, the whole batch is sent back.
Wiyot doesn't know it, but in the batch he is inspecting now, there are 100 products and 16 are defective. If he samples 4 products from this batch without replacement,what is the
a) All of the products in the sample will be defective?
b) None of the products in the sample are defective?
c) At least one of the products is defective and the whole batch is sent back?
For all of the above, round to four decimal places.
answer a,b, and c
Here they gave a group of 100 products and out of them 14 are defective hence there will be = 86 non defective onces. Instead of checking all products samples of 4 are sent for inspection and if even one is a found to be defective, the batch will be rejected.
Since we are choosing randomly a fixed number from a big group without replacement , we will use the combination function since the order of selection is not important.
Ways of choosing 'r' items from 'n' =
for the start we are choosing any 4 products from the 100 = 100C4 = 3921225
This will include all possibilities that 0 , 1, 2, 3, 4 are defectives
Probability is the numerical value given to a chance of an event happening. It is generally calculated as
Probability = No. of desired events / total outcomes
Total outcomes will be any how choosing 4 out of 100 = 3921225
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