Probability Basics

Measuring how likely something is.

12 problems · about 20 minutes · TEKS P.S.2.A, S-CP.A.1

What this lesson teaches

The student computes theoretical and experimental probabilities and applies the complement rule.

Probability runs from 0 to 1.
Theoretical probability counts outcomes; experimental probability counts results.
The complement rule turns "at least one" into a single subtraction.

Straightforward practice. Get the method working first.

5 problems

P(A) = 0.45. What is P(not A)?
Answer 0.55
Why 0.55.
After four heads, what is the chance of heads next?
Answer Still one half; the coin has no memory.
Why Still 0.5.
One die. Probability of a six, as a decimal to three places?
Answer 0.167
Why 1 ÷ 6.
One die. Probability of an even number, as a decimal?
Answer 0.5
Why 3 of 6.
P(A) = 0.2. What is P(not A)?
Answer 0.8
Why 1 − 0.2.

The same ideas with more to keep track of.

3 problems

A bag has 4 red and 6 blue. Probability of blue, as a decimal?
Answer 0.6
Why 6 of 10.
20 trials gave 13 successes. Experimental probability, as a decimal?
Answer 0.65
Why 13 ÷ 20.
Five heads in a row. Probability the next toss is tails, as a decimal?
Answer 0.5
Why A coin has no memory.

Mixed problems. Work out what kind of question it is before you start.

4 problems

Sort each probability by what it describes.
Answer Theoretical: One in six for a die, by counting faces, Half for a coin, by counting sides · Experimental: 13 heads in 20 actual tosses, 47 sixes in 300 actual rolls
Why One counts possibilities; the other counts what happened.
What is the probability of an impossible event?
Answer 0
Why The bottom of the scale.
The Bag: A bag has 3 red and 7 blue marbles. What is the probability of red, as a decimal?
Answer 0.3
Why 0.3.
The Complement: The probability of rain is 0.35. What is the probability of no rain?
Answer 0.65
Why 0.65.