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