These should help!! The corresponding vertices make a rectangular prism:)
Fifty students in the fourth grade class listed their hair and eye colors in the table below: Brown hair Blonde hair Total Green
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Given the table below showing t<span>he
probabilities of the orphaned pets in six cities' animal shelters being
different types of animals.
</span>
City Cat Dog Dog Dog <span>Dog
−Lhasa Apso −Mastiff −Chihuahua −Collie
Austin 24.5% 2.76% 2.86% 3.44% 2.65%
Baltimore 19.9% 3.37% 3.22% 3.31% 2.85%
Charlotte 33.7% 3.25% 3.17% 2.89% 3.33%
St. Louis 43.8% 2.65% 2.46% 3.67% 2.91%
Salt Lake
City 28.9% 2.85% 2.78% 2.96% 2.46%
Orlando 37.6% 3.33% 3.41% 3.45% 2.78%
Total 22.9% 2.91% 2.68% 3.09% 2.58%</span><span>
Condtional probability </span><span>is a measure of the probability of an event given that another event has occurred. If the event of interest is A and the event B is known or assumed to have occurred, "the conditional probability of A given B", or "the probability of A under the condition B", is usually written as P(A|B).
The probability of A given B, is given by
From the table, the probability that an </span>orphaned pet in a St. Louis animal shelter is a mastiff dog is 2.46% and the probability that <span>an <span>orphaned pet in a St. Louis animal shelter is a dog is 2.91% + 2.68% + 3.09% + 2.58% = 11.26%</span>
The probability that a randomly selected orphaned pet in a St. Louis animal shelter is a mastiff given that it is a dog, is given by
</span>
</span>
City Cat Dog Dog Dog <span>Dog
−Lhasa Apso −Mastiff −Chihuahua −Collie
Austin 24.5% 2.76% 2.86% 3.44% 2.65%
Baltimore 19.9% 3.37% 3.22% 3.31% 2.85%
Charlotte 33.7% 3.25% 3.17% 2.89% 3.33%
St. Louis 43.8% 2.65% 2.46% 3.67% 2.91%
Salt Lake
City 28.9% 2.85% 2.78% 2.96% 2.46%
Orlando 37.6% 3.33% 3.41% 3.45% 2.78%
Total 22.9% 2.91% 2.68% 3.09% 2.58%</span><span>
Condtional probability </span><span>is a measure of the probability of an event given that another event has occurred. If the event of interest is A and the event B is known or assumed to have occurred, "the conditional probability of A given B", or "the probability of A under the condition B", is usually written as P(A|B).
The probability of A given B, is given by
From the table, the probability that an </span>orphaned pet in a St. Louis animal shelter is a mastiff dog is 2.46% and the probability that <span>an <span>orphaned pet in a St. Louis animal shelter is a dog is 2.91% + 2.68% + 3.09% + 2.58% = 11.26%</span>
The probability that a randomly selected orphaned pet in a St. Louis animal shelter is a mastiff given that it is a dog, is given by
Answer:
The answer is below
Step-by-step explanation:
A sugar refinery has three processing plants, all receiving raw sugar in bulk. The amount of raw sugar (in tons) that one plant can process in one day can be modelled using an exponential distribution with mean of 4 tons for each of three plants. If each plant operates independently,a.Find the probability that any given plant processes more than 5 tons of raw sugar on a given day.b.Find the probability that exactly two of the three plants process more than 5 tons of raw sugar on a given day.c.How much raw sugar should be stocked for the plant each day so that the chance of running out of the raw sugar is only 0.05?
Answer: The mean (μ) of the plants is 4 tons. The probability density function of an exponential distribution is given by:
a) P(x > 5) =
b) Probability that exactly two of the three plants process more than 5 tons of raw sugar on a given day can be solved when considered as a binomial.
That is P(2 of the three plant use more than five tons) = C(3,2) × [P(x > 5)]² × (1-P(x > 5)) = 3(0.2865²)(1-0.2865) = 0.1757
c) Let b be the amount of raw sugar should be stocked for the plant each day.
P(x > a) =
But P(x > a) = 0.05
Therefore:
a ≅ 12