2. There is a 50% chance that you will study for the exam and earn the...

2. There is a 50% chance that you will study for the exam and earn the highest grade in the class, and a 75% chance that you will earn the highest grade in the class.

Q The probability that you will study for the exam given that you earn the highest grade in the class is:

3. Cast two dice (one red, and one green) and add the numbers facing up. Let

E: The green die shows 2 .
F: The sum is 5 .
P(E|F) =

P(F|E) =

Solutions

Expert Solution

Given that

P(study for the exam and highest grade) = 0.50

P(highest grade) = 0.75

The probability that you will study for the exam given that you earn the highest grade in the class is:

P(study for the exam | highest grade) =P(study for the exam and highest grade) /P(highest grade) = 0.50 /0.75 = 0.6667

Following is the possible outcomes when we sum the outcomes of rolls of two dice:

In each of the outcome first outcome is of green die and second outcome is of red die

Out of 36 outcome, 6 outcomes shows 2 on green die so

P(E) = 6 /36

Out of 36 outcome, 4 outcomes shows sum 5 so

P(F) = 4 /36

Out of 36 outcome, 1 outcome shows sum 5 and 2 on green die so

P(F and E) = 1 /36

----------------

P(E|F) = P(F and E) / P(F) = 1 / 4

P(F|E) = P(F and E) / P(E) = 1 / 6

orchestra answered 10 months ago

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