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Exercises Probability and the bell curve

Example 3.24 from Statistics, 3.5 Tree and Venn Diagrams

(part 5)

e. Using the tree diagram, calculate P(R on 2nd draw GIVEN B on 1st draw).

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
e. Given that a blue marble is selected first, we need only follow the left set of branches on the tree diagram. In this case, there are three ways to obtain red on the second draw and 11 possible outcomes.

Figure 3.11
$P (R on 2nd draw GIVEN B on 1st) = P (R on 2nd | B on 1st) = \frac{3}{11}$
You can also use the formula

$P (R on 2nd | B on 1st) = \frac{P (R on 2nd AND B on 1st)}{P (B on 1st)} = \frac{\frac{24}{121}}{\frac{64 + 24}{121}} = \frac{24}{88} = \frac{3}{11 .}$

How did it go?

Previous (part 4)Next (part 6)

From Statistics (High school edition) by OpenStax (Rice University), section 3.5, 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.