A student estimates that his probability of getting an A+ in any class is 0.95,
ID: 3828202 • Letter: A
Question
A student estimates that his probability of getting an A+ in any class is 0.95, independently of his other classes, where an A+ is worth 4.3 grade points. (a) If he takes 4 courses per semester, 2 semesters per year, and 4 years of courses, what is the chance that he has a perfect 4.3 grade point average? (b) In order for him to have a fifty-fifty chance (probability = 1/2) of having a perfect 4.3 GPA for his whole transcript, what would his probability of getting an A+ for each class have to be?
Explanation / Answer
Ans a:
Total number of classes are : 4(courses) * 2(semesters) * 4(years) = 32 classes.
Each class has probability of 0.95 for getting a A+.
Total probability of getting A+ in all 32 classes = 0.95 * 0.95 * ..... (32 times).
= (0.95) ^ 32
= 0.1937 (Answer)
Ans b:
We have 0.5 probability of getting a A+ in whole transcript.
Let 'x' be the probability of gettinng a A+ in one class.
Hence,
(x) ^ 32 = 0.5
therefore,
x = 0.9786 (Answer)
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