1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
grandymaker [24]
3 years ago
7

An internet search engine looks for a certain keyword in a sequence of independent web sites. It is believed that 20% of the sit

es contain this keyword. (a) Compute the probability that at least 5 of the first 10 sites contain the given keyword. (b) Compute the probability that the search engine had to visit at least 5 sites in order to find the first occurrence of a keyword.
Mathematics
1 answer:
marusya05 [52]3 years ago
4 0

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:

P(X=x)={10\choose x}0.20^{x}(1-0.20)^{10-x};\ x=0,1,2,3...

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)

              =1-\sum\limits^{4}_{x=0} {10\choose x}0.20^{x}(1-0.20)^{10-x}\\=1-0.1074-0.2684-0.3020-0.2013-0.0881\\=0.0328

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:

P(Y=y)=(1-p)^{x-1}p;\ x=1,2,3...

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)

             =1-\sum\limits^{4}_{x=1} (1-0.20)^{x-1}0.20\\=1-0.20-0.16-0.128-0.1024\\=0.4096

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.

You might be interested in
Determine the solution to the equation given 4(m-2)=18
Maksim231197 [3]

Answer:

m=13/2 hope this helped:)

Step-by-step explanation:

7 0
2 years ago
Is it increasing or decreasing? ( one answer only )
Shalnov [3]

Answer:

decreasing

Step-by-Step explanation:

5 0
2 years ago
Read 2 more answers
Evita lives 0.85 mile from her school . write this distance as a fraction in simplest form
gtnhenbr [62]
.85 is in the hundredths place so your fraction will be 85/100 then you divide it by 5 and get 17/20 as your answer. Hope this helps

3 0
3 years ago
Read 2 more answers
If p —&gt; q and q —&gt; r are true conditional statements,
kirill [66]

Answer:

False; this is the law of syllogism.

Step-by-step explanation:

Law of Detachment is:

1) p->q

2) p

------------------------

Conclusion: q

Law of syllogism is:

1) p->q

2) q->r

---------------------

Conclusion: p->r

8 0
3 years ago
A vector has a magnitude of 43
posledela

30.8 m

Step-by-step explanation:

Given: V = 43\:\text{m}, V_y = 30\:\text{m}

The x-component of vector \vec{\text{V}} is

V_x = \sqrt{V^2 - V_y^2} = \sqrt{(43)^2 - (30)^2} = 30.8\:\text{m}

5 0
2 years ago
Other questions:
  • Given that f(x) =3x^2 - 6x + 11 ,find the values of a,b and c for which f(x) = a(x - b)^2 + c
    14·1 answer
  • Which graph represents a quadratic function that has no real zeros?
    14·2 answers
  • Which will result in a perfect square trinomial?
    9·1 answer
  • It is 5 degrees outside and the temperature is expected to drop 4 degrees each hour for the next 3 hours. If this prediction is
    14·1 answer
  • how do i solve this. show all steps plz. this due very soon. help asap no idea what to do. ➡️MAKE SURE TO SHOW ALL STEPS!!!⬅️
    13·1 answer
  • Please (you'll get 25 pts)
    10·2 answers
  • (2m^(2)+5m^(4))+(6m+9m^(4))
    7·1 answer
  • Which statement is correct?
    11·1 answer
  • To make a fruit salad for a party, Chris
    8·1 answer
  • PLSSS help if you TURLY know THISS
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!