Understanding Probability

Probability is the branch of mathematics that quantifies uncertainty.

 

An experiment is any process with unpredictable results. Each repetition is a trial. Examples include flipping a coin or rolling a die.

 

An outcome is a single result of an experiment.

 

An event is a group of outcomes. A simple event consists of only one outcome.

 

The sample space encompasses all possible outcomes of an experiment.

Sample Problems

A.

1. Experiment: Rolling a die

Sample Space (S): S= {1, 2, 3, 4, 5, 6}  

Events (E): The event that even numbers appear. E=(2, 4, 6}

2. Experiment: Tossing a coin 

Sample Space (S): S= {H, T}

Events (E):The event that a head will occur.

E = {H}

3. Experiment: Rolling a die and tossing a coin.

Sample Space (S): S= {1H, 2H, 3H, 4H, 5H, 6H, 1T, 2T, 3T, 4T, 5T, 6T}

Events (E): The event that a tail and odd number will come out.

E= {1T, 3T, 5T}

Events (E): The event that a head and even will come out

E= {2H, 4H, 6H, 2T, 4T, 6T}

4. Experiment: Identical number cards (1, 2, ... 10) are placed in a box and a card is đrawn at random.

Sample Space (S): S= {1,2, 3, 4, 5, 6, 7, 8,9, 10}

Events (E): The event that the number drawn is a composite number.

E= {4, 6, 8, 10}

B. Write the sample space (S) for each experiment.

1) Tossing two coins S = {HH, HT, TH, TT}

2ⁿ = 2² = 4

2) Tossing three coins S= (HHH, HHT, HTH, HTT, TTT, THH, THT, TTH}

2ⁿ = 2³ = 8 

3) Rolling a pair of dice S = 6ⁿ = 6² = 36

(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)

(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)

(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)

(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)

(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)

(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)