Question

Suppose Nigel has a bag of colored wristbands,and he chooses one without looking. The bagcontains a total of25 wristbands and 6 ofthe wristbands are blue.


a.What is the probabilitythat Nigel will choose ablue wristband?

b.Is it likely, unlikely, or neither likely nor unlikelythat Nigel will choose a blue wristband?

A box contains four equal-sized cards labeled 1,3, 5, and 7. Tim will select one card from the box.

a.What is the probability that Tim will select acard labeled 4?

b.What is the probability that Tim will select acard labeled with a number less than 6?

c.What is the probability that Tim will select acard labeled with an odd number?

Model with MathHenry is going to color aspinner with 10 equal-sized sections. Three of thesections will be orange and 7 of the sections willbe purple. Is this spinner fair? If so, explain why. Ifnot, explain how to make it a fair spinner.

Higher Order ThinkingWithout being able tocalculate probability, describe the likelihood thatthe following event will occur.

All 21 students in a class share the samebirthday.


Assessment Practice

After many studies, a researcher finds that the probability that a wordrecognition app correctly interprets a handwritten word ismath
9
10
. Whichstatement is true?

𝖠It is impossible that the handwritten word will be correctly interpreted.

𝖡It is unlikely that the handwritten word will be correctly interpreted.

𝖢It is likely that the handwritten word will be correctly interpreted.

𝖣It is certain that the handwritten word will be correctly interpreted.

A bag contains 8 letter tiles of the same size. The tiles are labeledeither A, B, C, D, E, or F. Three of the tiles are labeled C. If Coreyselects 1 tile from the bag without looking, is the selection of lettersfair? Explain.

Answer 1

1) Nigel — 25 wristbands, 6 blue
a. Probability = 6/25 = 0.24 = 24%.
b. Since 24% < 50%, it is unlikely that he will choose a blue wristband.

2) Tim — cards {1, 3, 5, 7} (4 equally likely)
a. P(select 4) = 0 (no card labeled 4).
b. Numbers less than 6 are {1,3,5}: P = 3/4 = 0.75.
c. All cards are odd, so P(odd) = 4/4 = 1 (certain).

3) Spinner (10 equal sections: 3 orange, 7 purple)
- The sections are equal-sized, so each section is fair individually.
- But the color outcomes are not equally likely (orange 3/10, purple 7/10), so the spinner is not fair if “fair” means equal chance for each color.
- To make it fair by color, have 5 orange and 5 purple sections (or otherwise equalize counts).

4) All 21 students share the same birthday
- Extremely unlikely (practically impossible in everyday terms). The chance is vanishingly small.

5) Assessment practice — probability = 9/10
- 9/10 = 0.9, so it is likely the app will correctly interpret the handwritten word. Answer: C.

6) Bag of 8 letter tiles; three are C
- Not fair: P(C) = 3/8 while other letters (presumably) have smaller probabilities (e.g., 1/8). To make it fair, have the same number of tiles for each letter (or use one tile of each letter).