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) = _{n}C_{x}p^{x}(1p)^{nx}.
x 
P(x) 
_{n}C_{x}p^{x}(1p)^{nx} 

0 
.512 
_{3}C_{0}(.2)^{0}(.8)^{3} 
1(1)(.512) 
1 
.384 
_{3}C_{1}(.2)^{1}(.8)^{2} 
3(.2)(.64) 
2 
.096 
_{3}C_{2}(.2)^{2}(.8)^{1} 
3(.04)(.8) 
3 
.008 
_{3}C_{3}(.2)^{3}(.8)^{0} 
1(.008)(1) 
d) The probability of getting 2 or 3 right by guessing is