SOLUTION: a test consist of 10 true and false questions. To pass the test a student must answer at least eight questions correctly. If a student guess on each question, what is the probabili

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Question 350137: a test consist of 10 true and false questions. To pass the test a student must answer at least eight questions correctly. If a student guess on each question, what is the probability that the student will pass the test?
Found 2 solutions by edjones, ewatrrr:
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=.5 and y=.5
expand the binomial (x+y)^10
x^10+10x^9y+45x^8y^2=.0547 probability that the student will pass the test.
.
Ed

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
Hi
*
Note: The probability of x successes in n trials is:
.
P = C[10,8]* p%5Ex*q%5E%28n-x%29 where p and q are the probabilities of success and failure respectively. In this case both p & q are = 1/2 or .5
.
C[10,8] = +10%21%2F%288%21%2810-8%29%29%21=+10%21%2F%288%21%2A2%29%21=%2810%2A9%29%2F2+=45
.
P = 45%2A.5%5E8%2A.5%5E2+=+45%2A.0039%2A.25 = .0439
.
4.39% chance of getting 8 of the true and false questions correct