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yanalaym
1 month ago
12

A factory received a shipment of 38 sprockets, and the vendor who sold the items knows there are 5 sprockets in the shipment tha

t are defective. Before the receiving foreman accepts the delivery, he samples the shipment, and if too many of the sprockets in the sample are defective, he will refuse the shipment.
a) If a sample of 5 sockets is selected, find the probabilty that all in the sample are defective.
b) If a sample of 5 sprockets is selected, find the probability that none in the sample are defective.
Mathematics
1 answer:
tester [12.3K]1 month ago
5 0

Answer:

a) 0.00019923%

b) 47.28%

Step-by-step explanation:

a) To determine the likelihood that all sockets in the sample are defective, we can use the following approach:

The first socket is among a group that has 5 defective out of 38, leading to a probability of 5/38.

The second socket is then taken from a group of 4 defective out of 37, following the selection of the first defective socket, resulting in a probability of 4/37.

Extending this logic, the chance of having all 5 defective sockets is computed as: (5/38)*(4/37)*(3/36)*(2/35)*(1/34) = 0.0000019923 = 0.00019923%.

b) Using similar reasoning as in part a, the first socket has a probability of 33/38 of not being defective as it's chosen from a set where 33 sockets are functionally sound. The next socket has a proportion of 32/37, and this continues onward.

The overall probability calculates to (33/38)*(32/37)*(31/36)*(30/35)*(29/34) = 0.4728 = 47.28%.

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