SOLUTION: what is the probability of missing no more than 1 question by guessing on a 8 total true or false question test?

Question 930996: what is the probability of missing no more than 1 question by guessing on a 8 total true or false question test?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
This is a binomial distribution question.

n = 8
p = 1/2 = 0.5

Let's define the function B(k) to be the probability where the student misses k problems where . So it's defined in terms of the binomial distribution formula

B(k) = (n C k)*p^k*(1-p)^(n-k)

Let's plug in the constants n = 8 and p = 0.5 to get

B(k) = (8 C k)*0.5^k*(1-0.5)^(8-k)
B(k) = (8 C k)*0.5^k*0.5^(8-k)

Since it asks "what is the probability of missing no more than 1 question" we want to find P(X <= 1) which means we need to evaluate B(0) and B(1). Then we add up those two values

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P(Missing 0) = B(0) = (8 C 0)*(0.5^0)*(0.5)^(8-0) = 0.00390625

P(Missing 1) = B(1) = (8 C 1)*(0.5^1)*(0.5)^(8-1) = 0.03125

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Now add up the two individual probabilities (PDF's) to get the cumulative probability (CDF)

B(0) + B(1) = 0.00390625+0.03125 = 0.03515625

P(X <= 1) = 0.03515625

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So the probability of missing no more than 1 question is 0.03515625

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