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# Lesson Worksheet: Theoretical Probability Mathematics

In this worksheet, we will practice interpreting a data set by finding and evaluating the theoretical probabilities.

**Q1: **

A box contains 5 red marbles, 8 green marbles, and 4 yellow marbles. If a marble is picked from the box at random, what is the probability that the marble is red?

- A
- B
- C
- D
- E

**Q2: **

If this spinner is spun once, what is the probability of getting a vowel? Give your answer as a fraction in its simplest form.

- A
- B
- C
- D
- E

**Q3: **

A number is chosen at random from the set . What is the probability that the number is even?

- A
- B
- C
- D

**Q4: **

What is the probability of rolling a number greater than or equal to 4 on a fair die?

- A
- B0
- C
- D

**Q5: **

A bag contains an unknown number of balls. Given that one-sixth of the balls are white, one-fifth of them are green, and the rest are blue, what is the probability that a ball drawn at random from the bag is blue?

- A
- B
- C
- D

**Q6: **

A bag contains 30 colored marbles. The probability of choosing a white marble at random is . How many white marbles are in the bag?

**Q7: **

In a class of 50 students, 33 passed the mathematics test and 31 passed the language test. What is the probability that a randomly selected student failed in the language test?

- A
- B
- C
- D

**Q8: **

A class contains 59 students. In the class, the number of boys exceeds the number of girls by 7. If a student is chosen at random, what is the probability the student is a boy?

- A
- B
- C
- D

**Q9: **

A bag contains 7 pennies, 10 nickels, and 7 dimes. How many coins of each type should be added to increase the number of coins to 48, while keeping the probability of randomly selecting each type of coin the same?

- A8 pennies, 10 nickels, and 8 dimes
- B7 pennies, 7 nickels, and 7 dimes
- C9 pennies, 11 nickels, and 8 dimes
- D7 pennies, 7 nickels, and 10 dimes
- E7 pennies, 10 nickels, and 7 dimes

**Q10: **

A card is selected at random from a pack of 52 cards which are numbered 1 to 52. What is the probability that the selected card has a number which is neither a perfect square nor a multiple of 6?

- A
- B
- C
- D
- E