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Probability with a Table

You are taking two courses during winter session, math and history, and your subjective assessment of your performance is
Event Probability
fail both courses .05
fail math (irrespective of whether or not you fail history as well) .15
fail history (irrespective of whether or not you fail math as well) .08

Let's develop a joint-probability table to analyze this problem (the letters A - H represent probability values. For example, A is the probability of failing both math and history; B is the probability of failing math and passing history; while C is the sum of A and B, and represents the probability of failing math).

fail history pass history row sum
fail math A B C
pass math D E F
column sum G H

a) (3 pts.) What does C + F equal?
b) (3 pts.) What does A + B + D + E equal?
c) (12 pts) What is the probability of failing math only (that is, you fail math but pass history)?
d) (12 pts) What is the probability of passing either course?

Please assist with the attached problem.

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A Complete, Neat and Step-by-step Solution is provided in the attached Excel file.

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