probability

Question

A test consists of 20 problems, all with five-part multiple choice answers. A student guesses at each answer. What is the probability that she five or more correct?

It is asserted that 60% of the adults in a certain community are registered voters. If the 20 residents are selected randomly, what is the probability that eight or fewer will register?

Answer 1

(1) ANSWER: 37.04%

METHOD: The probability of selecting the correct answer by chance is ⅕=0.2 for each question. Let p=0.2 then q=1-p=0.8 (the probability of an incorrect guess).

(p+q)²⁰=1=p²⁰+20p¹⁹q+...+C(20,20-r)p²⁰⁻ʳqʳ+... for 0≤r≤20.

C(20,20-r)=C(20,r) by symmetry of the binomial expansion.

The probability of 5 or more correct is calculated by adding the first 16 terms. But it’s easier to sum the last 5 terms and subtract fro

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Comments

Network or system problems are preventing me from continuing with this double-question. I’ll try again tomorrow...