Test 27 (Lessons 53–54): Introduction to Probability Solutions

For problems 1–6, determine the probabilities using the fair spinner. Write answers in simplified form.

$P (vowel) = \frac{2}{6} = \frac{1}{3}$

Note

{A, E}

$P (even) = \frac{3}{6} = \frac{1}{2}$

Note

{2, 4, 6}

$P (C ‘) = 1 - \frac{1}{6} = \frac{5}{6}$

$P (C \cup 5) = \frac{1}{6} + \frac{1}{6} = \frac{2}{6} = \frac{1}{3}$

$P (odd \cup consonant) = \frac{3}{6} + \frac{4}{6} - \frac{1}{6} = 1$

Note

$Odd : {1, 3, 5}, Consonant : {B, C, D, F}$

Problem 5 is most likely to occur because the answer is one.

Construct a Venn diagram D to represent possible rolls of a single die containing the subsets: odd rolls and rolls greater than two.

For problems 8–10, use the two-way table.
A small survey was conducted at a college to determine where students and professors lived.

$360 + 6 + 75 + 84 = 525 P (student off campus) = \frac{75}{525} = \frac{1}{7}$

$P (student or professor on campus) = \frac{(360 + 6)}{525} = \frac{366}{525} = \frac{122}{175}$

$P (professor off campus) = \frac{6}{525} = \frac{2}{175}$

For problems 11–15, use the following scenario.

Ms. Liu’s class conducted an experiment by placing 20 cards in a bag. Each time a card was drawn, it was replaced before drawing another.

11–13) Find the probability of each card color to the nearest whole percent.

$74 + 88 + 82 = 244 P (red) = \frac{74}{244} = 0.303 = 30 % P (blue) = \frac{88}{244} = 0.361 = 36 % P (yellow) = \frac{82}{244} = 0.336 = 34 %$

Experiment Results

Ms. Liu says there are approximately the same number of each color card in the bag. Explain if the experiment was conducted fairly.

Sample: This is a fair experiment because the percentages are approximately the same for each color, and the tallies are very close together.

$Red : (0.30) (20) = 6 Blue : (0.36) (20) = 7.2 \approx 7 Yellow : (0.34) (20) = 6.8 \approx 7$

There are 6 red, 7 blue, and 7 yellow cards in the bag.