Question 367570
the probability that Loren will get an answer correct is 2/3.


the number of questions is 5.


the probability that she will get exactly 3 questions correct is (2/3)^3 * (1/3)^2


the probability that she will get exactly 4 questions correct is (2/3)^4 * (1/3)^1


the probability that she will get exactly 5 questions correct is (2/3)^5 * (1/3)^0


the number of ways that she can get 3 out of 5 questions correct is 5! / (2! * 3!) = 10


the number of ways that she can get 4 out of 5 questions correct is 5! / 4! * 1!) = 5


the number of ways that she can get 5 out of 5 questions correct = 1.


her total probability of getting at least 3 out of 5 questions correct is equal to:


[10 * (2/3)^3 * (1/3)^2] + [5 * (2/3)^4 * (1/3)^1] + [1 * (2/3)^5]


This is equivalent to:


.329218107 + .329218107 + .131687243 which is equal to .790123457