We need to see three things here

- 80% of chance of answer to be correct.
- So, 20% of chance of answer to be wrong.
- Probability that she will get ATLEAT two out of first three questions on her test correct.

Steps to answer question.

- Atleast two out of the first three questions on her test are correct, it means it can be more than 2 questions can be correct.
- So we have two possibilities. we can write it as P(Correct, correct, wrong) + P(All correct)
- Here, p( correct, correct, wrong) could be answered in 3 ways.let C as correct, W as wrong.
- We can answer two correct 1 wrong in 3 ways like P(c, w,c)+P(w,c,c)+P(c,c,w)
- We know atleast two are correct is P(c,w,c)+P(w,c,c)+P(c,c,w) +P(c,c,c)
- Now, use P(c)=80% =80/100 =0.8
- So, P(w) =1-0.8=0.2
- So, represent the corresponding probabilities, we get (0.8*0.2*0.8)+(0.2*0.8*0.8)+(0.8*0.8*0.2)+(0.8*0.8*0.8)
- Let’s simplify it, we get 0.128+0.128+0.128+0.512
- Simplify it further 0.896
- Let’s change it to percent by multiply the decimal 0.896 by 100%. We get 89.6%.