Fundamental Counting Principle Worksheet

**Page 1**

1.

Jim had a bag of marbles. There were 20 marbles in the bag: 6 red, 5 orange, 3 brown, 2 yellow, and 4 blue. Without looking, he chose a marble, recorded the color, and returned the marble to the bag. He performed this experiment 100 times and found that he chose a red marble 22 times. What was the experimental probability of choosing a red marble?

a. | $\frac{11}{10}$ | ||

b. | $\frac{1}{50}$ | ||

c. | $\frac{1}{5}$ | ||

d. | $\frac{11}{50}$ |

Correct answer : (4)

2.

A coin was tossed 60 times and 'Head' appeared 15 times. Find the experimental probability of tossing heads.

a. | $\frac{1}{8}$ | ||

b. | $\frac{3}{4}$ | ||

c. | $\frac{1}{2}$ | ||

d. | $\frac{1}{4}$ |

Correct answer : (4)

3.

Suppose you roll a number cube 10 times. You get an even number 3 times. Find the experimental probability that you get an even number.

a. | $\frac{1}{2}$ | ||

b. | $\frac{3}{5}$ | ||

c. | $\frac{3}{10}$ | ||

d. | $\frac{7}{10}$ |

Correct answer : (3)

4.

In how many ways can 3 pizza toppings be selected from a group of 7 toppings?

a. | 35 | ||

b. | 21 | ||

c. | 28 | ||

d. | 10 |

Correct answer : (1)

5.

A coin was tossed 8 times. The table shows the outcomes. What is the probability of getting a head?

a. | $\frac{1}{4}$ | ||

b. | $\frac{3}{4}$ | ||

c. | $\frac{5}{8}$ | ||

d. | $\frac{3}{8}$ |

Correct answer : (3)

6.

When the given spinner is spun, the theoretical probability of spinning ' A' is $\frac{2}{6}$. Tom spun the spinner four times and recorded the results in the table shown. Find the experimental probability and choose the expression that best compares the theoretical and experimental probability of spinning the alphabet 'A' on the spinner.

Ist Spin | IInd Spin | IIIrd Spin | IVth Spin |

B | C | B | A |

a. | $\frac{2}{6}$> $\frac{1}{4}$ | ||

b. | $\frac{2}{6}$= $\frac{1}{4}$ | ||

c. | Insufficient information | ||

d. | $\frac{2}{6}$< $\frac{1}{4}$ |

Correct answer : (1)

7.

The theoretical probability of getting the number '4' when a die is rolled is $\frac{1}{6}$. Ted rolled a die 5 times and recorded the results in the table shown.

Find the experimental probability and choose the expression that best compares the theoretical and experimental probability of getting the number '4' on the die.

I | II | III | IV | V |

4 | 4 | 5 | 3 | 6 |

a. | $\frac{1}{6}$ = $\frac{2}{5}$ | ||

b. | $\frac{1}{6}$ > $\frac{2}{5}$ | ||

c. | Insufficient information | ||

d. | $\frac{1}{6}$ < $\frac{2}{5}$ |

Correct answer : (4)

8.

The theoretical probability of getting an even number when a die is rolled is $\frac{3}{6}$. Jeff rolled a die 5 times and recorded the results in the table shown. Find the experimental probability and choose the expression that best compares the theoretical and experimental probability of getting an even number.

I | II | III | IV | V |

2 | 3 | 6 | 6 | 4 |

a. | $\frac{3}{6}$ < $\frac{4}{5}$ | ||

b. | $\frac{3}{6}$ > $\frac{4}{5}$ | ||

c. | Insufficient information | ||

d. | $\frac{3}{6}$ = $\frac{4}{5}$ |

Correct answer : (1)

9.

When the spinner shown is spun, the theoretical probability of spinning a 'composite number' is $\frac{6}{12}$. Bob spun the spinner 10 times and recorded the results in the table shown. Find the experimental probability and choose the expression that best compares the theoretical and experimental probability of spinning a 'composite number' on the spinner.

Numbers on the Spinner | Frequency |

8 | 3 |

1 | 2 |

4 | 1 |

7 | 4 |

a. | $\frac{6}{12}$ > $\frac{4}{10}$ | ||

b. | Insufficient information | ||

c. | $\frac{6}{12}$ < $\frac{4}{10}$ | ||

d. | $\frac{6}{12}$ = $\frac{4}{10}$ |

Correct answer : (1)

10.

When the spinner shown is spun, the theoretical probability of spinning an 'apple' is 50%. George spun the spinner five times and recorded the results in the table shown. Choose the expression that best compares the theoretical and experimental probability of spinning an 'apple' on the spinner.

1^{st} Spin | 2^{nd} Spin | 3^{rd} Spin | 4^{th} Spin | 5^{th} Spin |

Apple | Apple | Apple | Apple | Pear |

a. | Insufficient information | ||

b. | 50% > 80% | ||

c. | 50% = 80% | ||

d. | 50% < 80% |

Correct answer : (4)