Basic probability

What is this about?

Probability measures how likely something is to happen, with a number between 0 (impossible) and 1 (certain). When all outcomes are equally likely (like the faces of a die), you use Laplace's rule: favorable outcomes divided by possible outcomes.

Example 1

P(rolling a 3 with one die)

1. 1Possible outcomes: the die has 6 faces → 6 outcomes.
2. 2Favorable outcomes: only one face shows a 3 → 1 outcome.
3. 3Apply Laplace: P = 1 ÷ 6 = 1/6 ≈ 0.17.
4. 4It's closer to 0 than to 1: rolling one specific number isn't easy.

Result: 1/6

Example 2

P(drawing a red ball from a bag with 3 red and 2 blue)

1. 1Possible outcomes: 3 + 2 = 5 balls in total.
2. 2Favorable outcomes: 3 red balls.
3. 3P = 3 ÷ 5 = 3/5 = 0.6.
4. 4Since 0.6 is past the halfway mark, red is MORE likely than blue.

Result: 3/5

Practice exercises

Solve them in your notebook, then check the solution.

1. 1. When you roll a die, what is the probability of getting a number less than 4?

   Show the solution

   1/2

   A die has 6 faces. Favorable outcomes (a number less than 4): 1, 2, 3, that is, 3. P = 3/6 = 1/2 (simplified)

2. 2. When you roll a die, what is the probability of getting an odd number?

   Show the solution

   1/2

   A die has 6 faces. Favorable outcomes (an odd number): 1, 3, 5, that is, 3. P = 3/6 = 1/2 (simplified)

3. 3. In a class of 21 students, 19 wear glasses. If you pick one at random, what is the probability that they wear glasses?

   Show the solution

   19/21

   P = favorable outcomes / possible outcomes = 19/21

4. 4. A bag has 9 red balls and 9 blue balls. If you take one without looking, what is the probability that it's red?

   Show the solution

   1/2

   P = favorable outcomes / possible outcomes = 9/18 = 1/2 (simplified)

5. 5. A bag has 5 red balls and 7 blue balls. If you take one without looking, what is the probability that it's red?

   Show the solution

   5/12

   P = favorable outcomes / possible outcomes = 5/12