Unit E: Statistics and Probability

Chapter 2: Probability

Finding Probability Given Odds

If the odds in favour of an event are given, it is possible to find the probability.

Compare the ratios for odds and probability.

Odds in Favour	Probability
favourable outcomes : unfavourable outcomes	favourable outcomes : total outcomes

How are they similar? In both ratios, the number of favourable outcomes appears first.

How are they different? For the odds in favour ratio, the favourable outcomes are compared to the unfavourable outcomes. For probability, the favourable outcomes are compared to the total number of outcomes.

Example 7

The odds in favour of a cat having a litter of three healthy kittens are 10:1. Determine the probability of having a litter with three healthy kittens. Express the answer as a fraction.

Solution

In the question, the odds are given, which indicates favourable and unfavourable outcomes.

\begin{array}{rcl} odds in favour & = & number of litters with three healthy kittens : number of litters that do not have three healthy kittens \\ = & 10 : 1 \end{array}

Complete the table.

favourable outcomes (a litter than has 3 healthy kittens)	10
unfavourable outcomes (a litter that does not have 3 healthy kittens)	1
total outcomes	11

Notice that there is an additional line added to the table. Total outcomes is needed to calculate probability.

Find the probability using the probability formula.

\begin{array}{rcl} probability & = & \frac{number of litters with three healthy kittens}{total number of litters} \\ = & \frac{10}{11} \end{array}

The probability of a cat having a litter with three healthy kittens is

\frac{10}{11}

.

The probability can also be determined if the odds against are given. To avoid confusion, it is best to write the number of favourable, unfavourable, and total outcomes in a table.

Example 8

The odds against choosing a white jelly bean from a pile of jelly beans are 18:3. Determine the probability of choosing a white jelly bean from the pile. Express the answer as a fraction.

Solution

\begin{array}{rcl} odds against & = & number of unfavourable outcomes : number of favourable outcomes \\ = & 18 : 3 \end{array}

Complete the following table.

favourable outcomes (white jelly bean)	3
unfavourable outcomes (not a white jelly bean)	18
total outcomes	?

Calculate the probability.

\begin{array}{rcl} probability & = & \frac{number of white jelly beans}{total number of jelly beans} \\ = & \frac{3}{21} \\ = & \frac{1}{7} \end{array}

The probability of choosing a white jelly bean is

\frac{1}{7}