Question

When Hiroto is writing, there is 0.920.920, point, 92 probability that there will be no spelling mistakes on a page. One day, Hiroto writes an essay that is 111111 pages long.

Answer 1

Complete question :

When Hiroto is writing, there is 0.92 probability that there will be no spelling mistakes on a page. One day, Hiroto writes an essay that is 11 pages long.

Assuming that Hiroto is equally likely to have a spelling mistake on each of the 11 pages, what is the probability that he will have a spelling mistake on at least one of the pages?

Answer:

0.60

Step-by-step explanation:

The question meets the requirement for a binomial probability distribution :

Recall:

P(x = x) = nCx * p^x * q^(n-x)

Given :

Probability of making a spelling mistake = 1 - p(not making) = 1 - 0.92 = 0.08

Hence,

p = 0.08 ; q = 0.92

n = 11

P(x ≥ 1) = 1 - p(x = 0)

P(x = 0) = 11C0 * 0.08^0 * 0.92^11

P(x = 0) = 1 * 1 * 0.3996373778857415671808

P(x = 0) = 0.399

P(x ≥ 1) = 1 - p(x = 0)

P(x ≥ 1) = 1 - 0.399

P(x ≥ 1) = 0.601

P(x ≥ 1) = 0.60