Probability in Dance Competitions

The video tutorial explains how to calculate probabilities using a survey conducted at a dance studio. It covers the probability of students competing in various dance categories, using a Venn diagram to illustrate the results. The tutorial demonstrates how to calculate probabilities for students who have competed in none, all, or specific combinations of categories, and how to express these probabilities as fractions, decimals, and percentages.

What is the total number of students surveyed in the dance studio?

• 90

• 80

• 100

• 110

How many students have not competed in any dance category?

• 12

• 10

• 8

• 5

What is the simplified probability that a student has not competed in any category?

• 1/10

• 4/45

• 2/15

• 3/20

How many students have competed in all three dance categories?

• 11

• 10

• 12

• 9

What is the probability that a student has competed in all three categories as a percentage?

• 13.2%

• 10.2%

• 11.2%

• 12.2%

How many students have competed in smooth or standard but not rhythm?

• 31

• 29

• 27

• 25

What is the probability that a student has competed in smooth or standard but not rhythm as a decimal?

• 0.355

• 0.322

• 0.333

• 0.344

How many students have competed in rhythm and standard but not smooth?

• 11

• 12

• 13

• 14

What is the probability that a student has competed in rhythm and standard but not smooth as a percentage?

• 13.4%

• 16.4%

• 15.4%

• 14.4%

How many students have competed in rhythm?

• 52

• 50

• 51

• 53