Simple Probability

Probabilities are numbers expressed as ratios, fractions, decimals, or percents. They are determined by considering the results of an experiment. Simple probability is when we conduct a one stage or one object experiment. We choose an event, then the probability of that event is found by counting the number of times the event is true (favorable) and dividing by the total number of possible and equally likely outcomes.

P(event) =           number of true outcomes          
                     total number of equally likely outcomes


COIN
A common example is tossing a fair coin. There are two possible outcomes in the sample space S = {heads, tails}. The probability of event A = "tossing a head" is found by considering the number of true outcomes (head) divided by the number of possible outcomes (head/tail), or 1/2. Notice that probability of tossing a tail is also 1/2. We denote this as P(H) = 1/2 or P(T) = 1/2.

SPINNER

We can describe several probabilities using a spinner numbered with eight equal sections (so there are equally likely outcomes). Here the sample space is S = {1,2,3,4,5,6,7,8}.

P(5) = 1/8
The probability of spinning a five is one out of eight
P(even) = 4/8
The probability of spinning an even number is four out of eight
P(~ 3) = 7/8
The probability of apinning anything but three is seven out of eight
P(> 2) = 6/8
The probability of spinning a number greater than two is six out of eight
P(10) = 0
Spinning a ten is an impossible event
P(<10) = 8/8
Spinning a number less than ten is eight out of eight is certain

DICE
The probability of rolling a specific number on one fair die is 1/6. However, we also consider the probability of rolling a two or a six. We use the addition rule to add the probability of rolling a two (1/6) and the probability of rolling a six (1/6) to get the total probability P(2 or 6) = P(2) + P(6) = 2/6.