Multiply each binomial and find the coefficients.
1 answer:
Answers:
Row one: 1 and 1
Row two: 1, 2, and 1
Row three: 1, 3, 3, and 1
Row four: 1, 4, 6, 4, and 1
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Explanation:
Each value can be found in Pascal's triangle. You can also use the nCr combination formula to get each value. The nCr formula is
The value of n represents the row number. The r value is the column number, so to speak, for each row.
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Answer:
The probability is 0.971032
Step-by-step explanation:
The variable that says the number of components that fail during the useful life of the product follows a binomial distribution.
The Binomial distribution apply when we have n identical and independent events with a probability p of success and a probability 1-p of not success. Then, the probability that x of the n events are success is given by:
In this case, we have 2000 electronics components with a probability 0.005 of fail during the useful life of the product and a probability 0.995 that each component operates without failure during the useful life of the product. Then, the probability that x components of the 2000 fail is:
(eq. 1)
So, the probability that 5 or more of the original 2000 components fail during the useful life of the product is:
P(x ≥ 5) = P(5) + P(6) + ... + P(1999) + P(2000)
We can also calculated that as:
P(x ≥ 5) = 1 - P(x ≤ 4)
Where P(x ≤ 4) = P(0) + P(1) + P(2) + P(3) + P(4)
Then, if we calculate every probability using eq. 1, we get:
P(x ≤ 4) = 0.000044 + 0.000445 + 0.002235 + 0.007479 + 0.018765
P(x ≤ 4) = 0.028968
Finally, P(x ≥ 5) is:
P(x ≥ 5) = 1 - 0.028968
P(x ≥ 5) = 0.971032