Question

Alex is taking two courses; algebra and U.S. history. Student records indicate that the probability of passing algebra is 0.33, that of failing U.S. history is 0.33, and that of passing at least one of the two courses is 0.85. Find the probability of the following.

(a) Alex will pass history.


(b) Alex will pass both courses.


(c) Alex will fail both courses.


(d) Alex will pass exactly one course.

Answer 1

Let us define the following events:
A: Alex passes algebra; and

B: Alex passes U.S. History.

Now, we are given in question that: "The probability of passing algebra is 0.33"

=> P(A) = 0.33

Moreover, we are given that the probability of failing U.S. history is 0.33

Also, the probability of passing at least one of the two courses is 0.85

P(passing at least one of the two courses) = 0.85

=> P(passing algebra or passing U.S. history) = 0.85

=> P(A∪B) = 0.85

(a)

The probability that Alex will pass history is given by:

P(B) = 0.67 [ANSWER]

(b)

The probability that Alex will pass both courses is given by P(A∩B). Now, to find this probability note the following identity:

(c)

The probability that Alex will fail both courses is given by:

(d)

The probability that Alex will pass exactly one course is given by:

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