6. A student took a multiple choice test and guessed on three questions. Each question had 5 possible answers. Let x denote the number of correct answers.

a) What are n and p for this problem?

b) Complete the following probability distribution.

x

P(x)

0

1

2

3

c) Draw the histogram

d) What is the probability of getting 2 or 3 correct answers by guessing?

a) n is the number of times the experiment is repeated. In this case, the experiment is guessing on a question. There are 3 questions, so n = 3

p is the probability of success on any trial. If there are 5 possible answers and only 1 right one, then the probability of success is 1/5 = .2.

b) We use the formula P(x) = nCxpx(1-p)n-x.

x

P(x)

nCxpx(1-p)n-x

0

.512

3C0(.2)0(.8)3

1(1)(.512)

1

.384

3C1(.2)1(.8)2

3(.2)(.64)

2

.096

3C2(.2)2(.8)1

3(.04)(.8)

3

.008

3C3(.2)3(.8)0

1(.008)(1)

c) The histogram looks like

d) The probability of getting 2 or 3 right by guessing is

.096 + .008 = .104

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