A mathematics textbook has 100 pages on which typographical errors in the equations could occur. Suppose there are in fact two pages with errors. What is the probability that a random sample of 20 pages will contain at least one error?

Answer:0.0396Step-by-step explanation:the probability of one page having an error is p= 2/100 = 1/50if the letter q is the probability of not having an error then q = 49/50Using binomial probability:[tex]b(x;n,p) = \frac{n!}{x!(n-x)!}p^xq^{n-x}[/tex]n is the sample size--> n = 20And we want the probability that a random sample of 20 pages will contain at least one error, this is the same as 1 minus the probability of none of the 20 pages containing an error:probability(x ≥ 1) = 1 - probability( x = 0)Using the binomial probability equationProbability( x=0 ) =[tex]b(0;20,1/50) = \frac{20!}{0!(20-0)!}(1/50)^0(49/50)^{2-0}[/tex]Probability( x=0 ) =[tex]b(0;20,1/50) = (1)(1)(2401/2500)[/tex] = 0.9604Thus, probability(x ≥ 1) = 1 - 0.9604= 0.0396