1. A biology professor gives two assignments and a final in the course. The prof

Question

1. A biology professor gives two assignments and a final in the course.   The professor has noticed that 80% of students get a B or better on assignment 1. If a student gets a B or better on assignment 1 then chance of passing the final is 73%. If a student gets lower than a B on assignment 1 then there is a 45% chance of passing the final.

a) [3] Suppose a student passes the final. What is the probability that the student got C or lower on the first one? Write the question using function notation.

b) [3] What is the probability that a student passes the final? Write the question using function notation.

2. [3] Suppose the professor in question 1 polls five students to see if they liked the Biology book that was used for the course. Let the random variable X measure the number of students that say they liked the book. Write out the sample space for the variable X.

3. [3] The random variable X is uniformly distributed, such that 15 X 42. Calculate the following

P(X > 22 AND X < 35) =

4. [3] You are told that P(A) = 0.1 , P (B) = 0.15 and that the two events are independent. Calculate P(A OR B).

5. [3] You are told that events A, B are disjoint, with P(A) = 0.55   P(B) = 0.38. What is P(A and B) ?

Explanation / Answer

question 4)

P(A or B ) =P(a)+P(b)-P(aandb)

since A and B independent p( And B )=P(A)*P(B)

P(A or B) = P( A) +P(B)-P(A)*P(B)

             =0.1+0.15 - 0.015

             =0.235

5) igiven that A and B are disjoint

then P(A and B)= P(A)*PB) =0

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