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Exercises Probability and the bell curve

Example 3.22 from Statistics, 3.4 Contingency Tables

(part 3)

c. What is the probability that Muddy chooses Door One OR Door Two given that Muddy is caught by Alissa?

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.

Solution
c. This is a conditional probability, so consider only probabilities in the row labeled "Caught." Choosing Door One and choosing Door Two are mutually exclusive, so

$P (Choosing Door One OR Choosing Door Two AND Caught) = \frac{1}{15} + \frac{1}{12} = \frac{9}{60} .$
Use the formula for conditional probability $P (A | B) = \frac{P (A AND B)}{P (B)} .$
$P (Door One OR Door Two|Caught) = \frac{P (Door One OR Door Two AND Caught)}{P (Caught)} = \frac{\frac{9}{60}}{\frac{19}{60}} = \frac{9}{19.} .$

How did it go?

Previous (part 2)Next Contingency Tables: example 3.23

From Statistics (High school edition) by OpenStax (Rice University), section 3.4, 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.