Victoria is pretty good at math and has an 80% chance of getting any problem correct. What is the probability that she will get at least two out of the first three questions on her test correct?

We need to see three things here

  1. 80% of chance of answer to be correct.
  2. So, 20% of chance of answer to be wrong.
  3. Probability that she will get ATLEAT two out of first three questions on her test correct.

Steps to answer question.

  1. 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.
  2. So we have two possibilities. we can write it as P(Correct, correct, wrong) + P(All correct)
  3. Here, p( correct, correct, wrong) could be answered in 3 ways.let C as correct, W as wrong.
  4. We can answer two correct 1 wrong in 3 ways like P(c, w,c)+P(w,c,c)+P(c,c,w)
  5. We know atleast two are correct is P(c,w,c)+P(w,c,c)+P(c,c,w) +P(c,c,c)
  6. Now, use P(c)=80% =80/100 =0.8
  7. So, P(w) =1-0.8=0.2
  8. 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)
  9. Let’s simplify it, we get 0.128+0.128+0.128+0.512
  10. Simplify it further 0.896
  11. Let’s change it to percent by multiply the decimal 0.896 by 100%. We get 89.6%.

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