Solve by factoring: 1) x² + 6x + 8 = 0
2 answers:
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Answer:
(a) The probability that at least 5 of the first 10 sites contain the given keyword is 0.0328.
(b) The probability that the search engine had to visit at least 5 sites in order to find the first occurrence of a keyword is 0.4096.
Step-by-step explanation:
(a)
Let <em>X</em> = number of sites that contains the keyword.
The probability that a site contains the keyword is, <em>p</em> = 0.20.
The number of sites visited first is <em>n</em> = 10.
The random variable <em>X</em> follows a Binomial distribution with parameter <em>n</em> and <em>p</em>.
The probability mass function of <em>X</em> is:
Compute the probability that at least 5 of the first 10 sites contain the given keyword as follows:
P (X ≥ 5) = 1 - P (X < 5)
= 1 - P (X = 0) - P (X = 1) - P (X = 2) - P (X = 3) - P (X = 4)
Thus, the probability that at least 5 of the first 10 sites contain the given keyword is 0.0328.
(b)
Let <em>Y</em> = number of sites that contains the keyword.
The probability that a site contains the keyword is, <em>p</em> = 0.20.
The random variable <em>Y</em> follows a Geometric distribution with parameter <em>p</em>.
The probability mass function of <em>Y</em> is:
Compute the probability that the search engine had to visit at least 5 sites in order to find the first occurrence of a keyword as follows:
P (X ≥ 5) = 1 - P (X ≤ 4)
Thus, the probability that the search engine had to visit at least 5 sites in order to find the first occurrence of a keyword is 0.4096.
Well, the opposite of an exponent is a square root. However, in this case, it is to the power of 3. So in order to find p, you must do the cube root on both sides in order to get your answer: