Laws of Probability (Business)
Laws of Probability
The following two laws will be useful when carrying out probability calculations:
Multiplication Law - The probability of two independent events $A$ and $B$ both occurring at the same time can be written as:
\begin{equation} \mathrm{P}(A \; \text{and} \; B) = \mathrm{P}(A) \times \mathrm{P}(B) \end{equation}
Addition Law - The probability that either event $A$ or event $B$ will happen is given by:
\begin{equation} \mathrm{P}(A \; \text{or} \; B) = \mathrm{P}(A) + \mathrm{P}(B) - \mathrm{P}(A \; \text{and} \; B) \end{equation}
Worked Example 1
Worked Example
In Newcastle, $70\%$ of small businesses use the internet to advertise new products; $50\%$ of small businesses use flyers to advertise new products and a quarter of small businesses use both flyers and the internet.
(A) What is the probability that a randomly chosen small business in Newcastle uses either flyers or the internet to advertise new products?
(B) What is the proportion of small businesses in Newcastle that use neither the internet nor flyers to advertise new products?
Worked Example 2
Worked Example
$60\%$ of employees at a department store in Newcastle are women. Government research into methods of commuting to city jobs in the North East has shown on average that:$ \;$
- $12\%$ of people cycle into work.
- A quarter of the people drive.
- $10\%$ of people walk.
- And the rest use public transport.
What is the probability that a randomly selected employee of the department store in Newcastle commutes using public transport and is male?
Test Yourself
See Also
To develop these ideas further see the pages on discrete probability distributions and continuous probability distributions.