Question

assume that random guess are made for nine mutiple choice questions on physcis test, so that there are n=9 trials, each with probabilty of success(correct) given by p=0.25. a. find the probabilty that the number x of correct answers is at least 5. b. find the probabilty that the number x of correct answers is no more than 2

Answer 1

Ans:

Given that

n=9,p=0.25

P(x=r)=9C_r*0.25^r*(1-0.25)^9-r

x	p(x)
0	0.0751
1	0.2253
2	0.3003
3	0.2336
4	0.1168
5	0.0389
6	0.0087
7	0.0012
8	0.0001
9	0.0000

a)P(x>=5)=P(x=5)+P(x=6)+P(x=7)+P(x=8)+P(x=9)

=0.0389+0.0087+0.0012+0.0001+0.0000

=0.0489

b)P(x<=2)=P(x=0)+P(x=1)+P(x=2)=0.0751+0.2253+0.3003=0.6007