Question

The expected number of typographical errors on a page of a certain magazine is .2. What is the probability that an article of 10 pages contains (a) 0 and (b) 2 or more typographical errors?

Answer 1

a. 0.8187

b. 0.0176

Step-by-step explanation:

Given

Expected error = 0.2

Number of pages = 10

Let X = a random variable that denotes the number of typographical error in a magazine.

Suppose that there are x words in a page.

And there are p probability of a typographical error

We have that X ~ Binom(x,p)

a.

x = 10

E(X) = mean = λ = 0.2

To solve this, we'll make use of Poisson approximation of a binomial variable

i.e.

X ~ Pois(0.2)

P(X=x) = (λ^x e^-λ)/x!

For P(X=2)

P(X=2) = (0.2^0 * e^-0.2)/0!

P(X=2) = (1 * e^-0.2)/1

P(X=2) = e^-0.2

P(X=2) = 0.818730753077981

P(X=2) = 0.8187 ---------- Approximated

b.

P(X>=2) = 1 - P(X<2)

P(X>=2) = 1 - P(X=0) - P(X=1)

P(X=0) = 0.8187

Solving P(X=1)

P(X=1) = 0.2^1 * e^-0.2/1!

P(X=1) = 0.2e^-0.2

P(X=1) = 0.163746150615596

P(X=1) = 0.1637 ----------Approximated

So, P(X>=2) = 1 - 0.8187 - 0.1637

P(X>=2) = 0.0176