Respuesta :
Answer:
The probability of a selection of 50 pages will contain no errors is 0.368
The probability that the selection of the random pages will contain at least two errors is 0.2644
Step-by-step explanation:
From the information given:
Let q represent the no of typographical errors.
Suppose that there are exactly 10 such errors randomly located on a textbook of 500 pages. Let [tex]\mu[/tex] be the random variable that follows a Poisson distribution, then mean [tex]\mu = \dfrac{10}{500}= 0.02[/tex]
and the mean that the random selection of 50 pages will contain no error is [tex]\lambda = 50 \times 0.02 =1[/tex]
∴
[tex]Pr(q= 0) = \dfrac{e^{-1} (1)^0}{0!}[/tex]
Pr(q =0) = 0.368
The probability of a selection of 50 pages will contain no errors is 0.368
The probability that 50 randomly page contains at least 2 errors is computed as follows:
P(X ≥ 2) = 1 - P( X < 2)
P(X ≥ 2) = 1 - [ P(X = 0) + P (X =1 )] since it is less than 2
[tex]P(X \geq 2) = 1 - [ \dfrac{e^{-1} 1^0}{0!} +\dfrac{e^{-1} 1^1}{1!} ][/tex]
[tex]P(X \geq 2) = 1 - [0.3678 +0.3678][/tex]
[tex]P(X \geq 2) = 1 -0.7356[/tex]
P(X ≥ 2) = 0.2644
The probability that the selection of the random pages will contain at least two errors is 0.2644
The possibility of a random selection of 50 pages will contain at least two errors is [tex]0.264242[/tex].
To understand the calculations, check below
Probability:
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are to happen, using it.
Let [tex]X[/tex] denotes the number of errors on [tex]50[/tex] randomly selected pages.
[tex]X\sim Poisson(\frac{50}{500}\ast 10)[/tex] or [tex]X\sim Poisson(1)[/tex]
The probability mass function of [tex]X[/tex] is,
[tex]P\left ( X=x \right )=\frac{e^{-1}\ast 1^{x}}{x!}=0,1,2...[/tex]
Now,
The probability that a random selection of [tex]50[/tex] pages will contain no errors,
[tex]=P\left ( X=0 \right ) \\ =\frac{e^{1}\ast 1^{0}}{0!} \\ =0.367879[/tex]
Learn more about the topic of Probability: https://brainly.com/question/19032615
