Question

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 1

Answer:

The probabability is $\frac{85}{100} =0.850$

Step-by-step explanation:

We are going to suppose that each score has the same probability.

For example :

$P(66) = P(89)$

Where P(66) is the probability of score a 66 and P(89) is the probability of score an 89

If A is a certain score :

$P(A) = \frac{CasesWhereAOccurs}{Total Cases}$

In the exercise :

$P(1) = P(2)=...=P(100)=\frac{1}{100} =0.01$

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

$P(1) + P(2) + ... + P(85) =\frac{1}{100} +\frac{1}{100} +...+\frac{1}{100} =(85).\frac{1}{100} \\P(Not Score Higher Than An 85)=\frac{85}{100}$