5. Bart is a student in a History class. In order for Bart to receive an A grade for the course, he must score higher than an 85 on the final exam (out of a possible 1 to 100 score). What is the probability that Bart will not score higher than an 85 and receive an A in the course ?

Answer:The probabability is [tex]\frac{85}{100} =0.850[/tex]Step-by-step explanation:We are going to suppose that each score has the same probability.For example :[tex]P(66) = P(89)[/tex]Where P(66) is the probability of score a 66 and P(89) is the probability of score an 89If A is a certain score :[tex]P(A) = \frac{CasesWhereAOccurs}{Total Cases}[/tex]In the exercise :[tex]P(1) = P(2)=...=P(100)=\frac{1}{100} =0.01[/tex]Bart must score higher than an 85 on the final exam.We are looking for the probability of the event : ''Bart obtains a 1 or a 2 or ... or a 85''This can be written in terms of events as :P(1∪2∪...∪85) = P(1) + P(2) + ... + P(85)As we consider each event as independent[tex]P(1) + P(2) + ... + P(85) =\frac{1}{100} +\frac{1}{100} +...+\frac{1}{100} =(85).\frac{1}{100} \\P(Not Score Higher Than An 85)=\frac{85}{100}[/tex]