Moderate# Discrete Probabilities with Failing Students

STATS-EZUFF0

Consider the following diagram which assigns probabilities to the number of students that will fail a certain Statistics class in a given semester.

How many of the following statements must be true?

i.The probability that an even number of students fail the class is virtually equal to .45

ii.The chance that at least 4 students fail the class is less than 20%.

iii.There are 5 students in the class

iv.At least 1 student fails the class

v.Suppose the professor failed 3 students in the previous semester. Let $Y$ be the number of students the professor fails in these two semesters. $P(Y<5.5)=.7$