A student is prone to migraine headaches, which do not happen often, do not last long, but are completely unpredictable; and keep the student from coming to class that day. The probability of a headache on a given day is only 05. a) It is the beginning of the semester. What is the probability that the first missed class for a headache wil take place on the 12th class day? b) The student has missed none of the first 10 class days of the semester. What is the probability the student will have missed none of the first 25 class days of the semester?

a) 0.02844

b) 0.4633

Step-by-step explanation:

Probability of having an headache = Probability of missing a class = 0.05

Probability of not having an headache = Probability of not missing a class = 1 - 0.05 = 0.95

a) Probability of missing only the 12th day after 11 days of not missing a class due to headache = (0.95) ¹¹ (0.05) = 0.02844

b) Given that the student has missed none of the first 10 class days of the semester. The probability the student will have missed none of the first 25 class days of the semester is a conditional probability given by

(Probability of not missing the first 10 days and 25 days of school) / (Probability of not missing the first 10 days of school)

Probability of not missing the first 10 days and 25 days of school = Probability of not missing the first 25 days of school = (0.95) ²⁵ = 0.2774

Probability of not missing the first 10 days of school = (0.95) ¹⁰ = 0.5987

Given that the student has missed none of the first 10 class days of the semester. The probability the student will have missed none of the first 25 class days of the semester = 0.2774/0.5987 = 0.4633