Probability — Quiz 4

Questions in this quiz (10)

1. A code for an entry system requires exactly 8 characters. Each character can either be one of the 26 lowercase letters from a to z or one of the 10 digits from 0 to 9. The first character must be a digit and the last character must be a letter. How many different possible codes are there?

   • $$36^6 \times 26$$
   • $$10 \times 36^6 \times 26$$
   • $$10 \times 36^6$$
   • $$36^6$$

2. A two-digit number from 10 to 99, inclusive, is chosen at random. What is the probability that the number is divisible by 4?

   • $$\frac{11}{90}$$
   • $$\frac{11}{45}$$
   • $$\frac{12}{45}$$
   • $$\frac{24}{45}$$

3. Sets $$A$$, $$B$$, and $$C$$ are defined below:$$A = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$$$$B = \{3, 5, 7, 9\}$$$$C = \{2, 3, 9\}$$A number is randomly selected from $$A$$. What is the probability that the selected number will be an element of both $$B$$ and $$C$$?

   • $$\frac{1}{5}$$
   • $$\frac{1}{10}$$
   • $$\frac{1}{3}$$
   • $$\frac{1}{2}$$

4. Of 15 people in a group, how many ways can you select a Captain, Vice Captain, and Secretary?

   • 2100
   • 2730
   • 2650
   • 2200

5. How many distinct permutations of the letters in the word $$eeefffggg$$ are there?

   • 1680
   • 210
   • 560
   • 243

6. A security code consists of 2 letters (a-z) followed by 3 digits (0-9), and no letter or digit can be repeated. How many possible codes are there?

   • 67,600
   • 65,000
   • 58,500
   • 468,800

7. How many more unique 4-letter codes can you create from the letters A, B, C, D, E, F if repetition is allowed compared to when repetition is not allowed?

   • 1656
   • 360
   • 1296
   • 936

8. In a jar, there are six balls numbered 1 to 6. Jane randomly picks two balls without replacement. What is the probability that the sum of the numbers on the balls is 7?

   • $$\frac{4}{5}$$
   • $$\frac{4}{15}$$
   • $$\frac{1}{5}$$
   • $$\frac{3}{5}$$

9. If the probability that Team A wins each game against Team B is 0.6, and the games are independent events, what is the probability that Team A wins all 4 games in a 4-game series?

   • $$0.216$$
   • $$0.13$$
   • $$0.6$$
   • $$0.36$$

10. Samantha is taking a science quiz and has 2 minutes left. She randomly guesses the answers to 4 multiple-choice questions, each with 5 options. What is the probability that she gets at least 1 of those questions correct?

    • $$\frac{369}{625}$$
    • $$\frac{4}{5}$$
    • $$\frac{64}{625}$$
    • $$\frac{3}{5}$$