a computer network a virus is spreading from machine to machine. Each week, the proportion of uninfected computers that remain uninfected is 0.65 with the rest becoming infected. Meanwhile, 0.20 of the computers

About 45% of students participate in a community volunteer program outside of school. If 50 students are selected at random, find the probability that at most 25 of them participate in a community volunteer program outside of school.

A study tracked a large group of people for 10 years. At the start of the study, 20% were heavy smokers (H), 30% were light smokers (L), and 50% were non-smokers (N). The interest of the study was whether the people in the study died during the study (D) or not die (Dc ). The probability that a light smoker died during the study was twice that of the probability of a non-smoker dying. Also, the probability that light smoker died during the study was half that of the probability of a heavy smoker dying. A randomly selected person from the study died during the study. What is the probability that this person was a heavy smoker (given they died, what is the probability they were a heavy smoker H)?

In a recent poll of voters, 20% were displeased with both candidates. If 3 people were picked at random. find the probability that at least one liked one of the candidates.