Ratios, Proportions,Rates, and Probability

Ratios

Can be verbal, such as ratio of cats to dogs is 3 to 4
Using colons 3:4
Fractional form ratios 3/4

Part to Part ratio & Part to whole ratio

12 male students and 21 female students
12/21=4/7
part to whole of male to all the students in the class
12/12+21= 12/33= 4/11

Proportion

an equation of two ratios that shows the comparative relationship between parts things or elements with respect to size, amount, or degree.

Rate

is simply a ratio that compares two different but related quantities, such as a distance divided by time, or amount divided by time, or cost per unit.

In other words:
Rate=Distance/Time
Rate= Amount/ Time
Rate= Cost/Units

Another way rates is to think of them as changes in the numerator per changes in the denominator. For instance, if your rate of pay is $15/hour, you know that if you work one more hour you will earn an additional $15.

The key to solving rate problems is to set them up as proportions. Convert the units if necessary and solve for the unknown value.

Close attention to units and ratios and proportions.

Probability

likelihood that a particular event will occur.
To find the probability that something is going to happen, use this formula:
Probability= Number of Outcomes of Interest / Number of Possible outcomes

Ways of probability

can be expressed as a fraction, a decimal, or a percent

Probabilities are

always between 0 and 1 (or between 0% and 100%)

Probability of 0 means

that there are NO outcomes of interest

Probability of 1 means

that all the possible outcomes result in the outcome of interest occurring

probability of 2 events occurring together

find the probability that the first event occurs and multiply this by the probability that the second event occurs. The probability of two independent events both occurring will be less than the probability of either occurring by itself.

probability of 1 or another event occurring

add the individual probabilities.
The probability of one or another event occurring will be greater than the probability of either event occurring alone.