Virginia SOL Math / Grade 7 / Probability & Statistics

7.PS.1

Experimental & Theoretical Probability

What you'll learn

  • Find theoretical probability of a simple event
  • Find experimental probability from data
  • Compare experimental and theoretical probability

Words to know

Probability —
a number from 0 to 1 that tells how likely an event is
Theoretical probability —
what should happen based on equally likely outcomes
Experimental probability —
what actually happened, found from trials
Outcome —
one possible result of an experiment
Event —
a set of one or more outcomes

Why it matters Probability helps us judge chances in games, weather forecasts, and decisions, and comparing theory to experiment shows how results settle over many trials.

Worked examples

Model ItI do

A number cube is rolled. What is the theoretical probability of rolling a 4?

There is 1 favorable outcome and 6 equally likely outcomes. The probability is 1 over 6.

Try It TogetherWe do

A coin is flipped 20 times and lands heads 12 times. Find the experimental probability of heads.

Divide heads by total flips: 12 over 20, which simplifies to 3 over 5. The experimental probability of heads is 3 over 5.

Now YouYou do

A spinner has 4 equal sections colored red, blue, green, and yellow. Find the theoretical probability of landing on green.

Count the favorable sections over the total sections. Check your answer in the back of this chapter.

Practice

Mastered 0 of 11

Warm-up

Ease in with the basics.

  1. 1.A coin is flipped. What is the theoretical probability of heads?

  2. 2.A number cube is rolled. What is the theoretical probability of rolling a 3?

  3. 3.A bag has 4 red and 6 blue marbles. What is the probability of drawing red?

On Level

The core Quick Check from the book.

  1. 1.A number cube is rolled. Find the theoretical probability of rolling an even number.

  2. 2.A bag has 3 red and 2 blue marbles. Find the probability of drawing red.

  3. 3.In 50 spins, a spinner lands on red 10 times. Find the experimental probability of red.

  4. 4.What is the probability of an event that is certain?

  5. 5.A coin is flipped. Find the theoretical probability of tails.

Challenge

Stretch your thinking.

  1. 1.A spinner is spun 40 times and lands on green 8 times. Find the experimental probability of green as a fraction in simplest form.

  2. 2.The theoretical probability of rolling a 5 on a number cube is 1 over 6. In 60 rolls, how many 5s would you expect?

  3. 3.A number cube is rolled 30 times and a 2 comes up 9 times. Is the experimental probability of a 2 greater than or less than the theoretical probability?