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Exercises Probability and the bell curve

Example 3.10 from Statistics, 3.2 Independent and Mutually Exclusive Events

Independent and Mutually Exclusive Events: example 3.10

Let event C = taking an English class. Let event D = taking a speech class.

Suppose P(C) = .75, P(D) = .3, P(C|D) = .75 and P(C AND D) = .225.

Justify your answers to the following questions numerically.

Are C and D independent?
Are C and D mutually exclusive?
What is P(D|C)?

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

1
Solution
1. Yes, because P(C|D) = .75 = P(C).
2. No, because P(C AND D) is not equal to zero.
3. P(D|C) = $\frac{P (C AND D)}{P (C)}$ = $\frac{0 .225}{.75}$ = .3

How did it go?

Previous (part 2)Next Independent and Mutually Exclusive Events: example 3.12

From Statistics (High school edition) by OpenStax (Rice University), section 3.2, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.