If A = {1, 2, 3} and B = {1, 2, 2, 3}, is B ⊆ A? If so, is A = B?
1 answer:
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ANSWER:
22
(All you’re doing is plugging in the values into the formula)
22
(All you’re doing is plugging in the values into the formula)
Answer:
a) 0.984
b) 20 people
Step-by-step explanation:
a)
If The probability that a person carries the gene is 0.1, then in a sample of 20 people, 2 should carry the gene.
Now, we want to know how many samples there are with this property.
Since we have 20 elements where 18 are alike (do not carry the gene) and 2 are alike (carry the gene), we have to compute the number of permutations of 20 elements in which 18 are alike and 2 are alike. This number is
In this 190 20-tuples there are only 3 where the 2 carriers of the gene are in the first 3 places, namely
(1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0)
(1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0)
(0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0)
where 1=carries the gene, 0=does not carry the gene.
So there are 190-3 = 187 elements in which the first 3 elements have no 2 carriers, hence the probability that 4 or more people will have to be tested until 2 of them with the gene are detected is 187/190 = 0.984 (98.4%) rounded to three decimal places.
b)
Given that the probability that a person carries the gene is 0.1, then in a sample of 20 people, 20*0.1 = 2 should carry the gene.
Answer:
Step-by-step explanation:
<u>Given Second-Order Homogenous Differential Equation</u>
<u>Use Auxiliary Equation</u>
<u />
<u>General Solution</u>
<u />
Note that the DE has two distinct complex solutions where
and
are arbitrary constants.