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a test contains 20 true or false, For each problem, the student: A)knows the answer with probability 0.88 B)thinks she knows the answer but is wrong...

a test contains 20 true or false, For each problem, the student:


A)knows the answer with probability 0.88

B)thinks she knows the answer but is wrong with probability 0.03,

C)is aware of the fact that she doesn't know the answer with probability 0.09.


Assume that these alternatives happen independently for each question. If the student is aware of not knowing the answer, she guesses true or false at random and is correct with probability 1/2.


  1. What is the probability the student will get at least 19 questions out of 20? 
  2. Let X be the number of consecutive problems answered correctly at the beginning of the test before the first incorrect one Find P(X=5)?
  3. Find P(5≤X≤10)?

 

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