the probability of a computer memory chip being defective is 0.02. which of ghe following statements is true?
a) in a shipment of 1000 chips, it is certain that at least one will be defective.
b) in a shipment of 100 chips, two will be defective
c)the expected number of chips in a shipment of 500 is 10
d)None of the above
None of the above
These are probabilities; no outcome is certain. "Will'
infers certainty.
Your third choice does not make sense. You need to proofread your questions before you post them.
From you data, I would pick d.
Shuta kayo mali ang sagot na none of the above 😅,
B po ang sagot
b)
d) None of the above
To determine which of the statements is true, we will analyze each one individually based on the given probability of a computer memory chip being defective.
a) In a shipment of 1000 chips, it is certain that at least one will be defective.
To check the probability of at least one defective chip in a shipment of 1000, we can calculate the probability of no defective chips and subtract it from 1:
P(no defective chips) = (1 - probability of a chip being defective)^number of chips
P(no defective chips) = (1 - 0.02)^1000 ≈ 0.135
Therefore, the probability of having at least one defective chip = 1 - 0.135 ≈ 0.865.
This means that it is almost certain (not 100% certain) to have at least one defective chip in a shipment of 1000. So, statement a) is true.
b) In a shipment of 100 chips, two will be defective.
To check the probability of having two defective chips in a shipment of 100, we can calculate the probability using the binomial distribution formula:
P(exactly two defective chips) = (number of ways to choose 2 defective chips out of 100) * (probability of a chip being defective)^2 * (probability of a chip not being defective)^(remaining chips)
P(exactly two defective chips) = (100 choose 2) * (0.02)^2 * (0.98)^(98) ≈ 0.270
Therefore, the probability of having exactly two defective chips in a shipment of 100 is approximately 0.270. So, statement b) is false.
c) The expected number of chips in a shipment of 500 is 10.
The expected number of defective chips in a shipment can be calculated by multiplying the total number of chips by the probability of a chip being defective:
Expected number of defective chips = total number of chips * probability of a chip being defective
Expected number of defective chips = 500 * 0.02 = 10
Therefore, the expected number of defective chips in a shipment of 500 is indeed 10. So, statement c) is true.
Based on our analysis, the correct statement is:
c) The expected number of chips in a shipment of 500 is 10.