Question

a jar contains 36 disks: 9 each of four colors - red, green, blue, and yellow. each set of disks of the same color is numbered from 1 to 9. suppose you draw one disk at random from the jar. define events b: get a blue disk, and n: get a disk with the number 8.
(a) make a two - way table that displays the sample space in terms of events b and n.
(b) find p(b). (round to 2 decimal places. leave your answer in decimal form.)
find p(n). (round to 3 decimal places. leave your answer in decimal form.)
(c) find the probability of getting a blue n. (round to 3 decimal places. leave your answer in decimal form.)
(d) explain why p(b ∪ n) ≠ p(b) + p(n).
the events \disk is blue\ and \disk is the number eight\ are not mutually exclusive. these two events can occur at the same time.
use the general addition rule to compute p(b ∪ n). (round to 3 decimal places. leave your answer in decimal form.)

Explanation:

Step1: Recall the general addition rule

The general addition rule is \(P(B\cup E)=P(B)+P(E)-P(B\cap E)\)

Step2: Substitute the known values

We know \(P(B) = 0.25\), \(P(E)=0.111\), and \(P(B\cap E) = 0.028\)

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Answer:

\(0.333\)