AND / OR Rules

This lesson covers:

  1. The difference between 'independent events' and 'dependent events'
  2. The AND rule 
  3. The OR rule

Independent and dependent events


Independent events are events whose probability is not affected by the outcome of previous events.


For example, when flipping a coin you always have a 50% chance of getting a head - it doesn't matter if you got heads or tails last time, the probability is still 50%. 


Dependent events are events whose probability is affected by the outcome of previous events.


For example, if you have a bag of blue and red marbles and remove one at a time, the probability of picking a blue marble will change each time, as the number of marbles left in the bag decreases each time you remove one. 

If you roll multiple dice in a row, is the outcome of each event independent or dependent of the previous outcomes?

Independent

Dependent 

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A box contains 10 caramel and 10 mint chocolates. Max picks chocolates one at a time at random. 


Are the outcomes in this scenario (which chocolate Max picks each time) independent or dependent?

Independent

Dependent 

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AND rule


The AND rule is used to find the probability that two events will both happen. It only works if the events are independent.

To find the probability of two events both happening (for example event A AND event B), you just multiply their individual probabilities together. Mathematically you might write this as:


P(A AND B) = P(A) x P(B)

Example:


When flipping a coin and rolling a die at the same time, what is the probability of getting the results: 'tails' and '5'? 

We could write this as:


P(heads AND 5) = P(tails) x P(5)


P(heads AND  5) = 1/2 x 1/6 = 1/12


So the probability of flipping tails, and rolling a '5' is 1/12, or 8.33%.

Note: 


To use the 'AND' rule, the two events must be independent. 

When rolling two dice, what is the probability of getting a '3' on the first die and a '4' on the second die?


Give your answer as a fraction in its simplest form.

\frac{1}{36}

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When flipping a coin and rolling a die at the same time, what is the probability of getting both a 'heads' and an 'even number'?


Give your answer as a fraction in its simplest form.

\frac{1}{4}

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Each weekend Alisha plays netball and tennis. There is a 40% chance that her team wins netball, and a 70% chance that she wins her tennis match. 


What is the probability that she wins both the netball match and the tennis match?


Give your answer as a percentage.

28

%

%

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Each weekend Alisha plays netball and tennis. There is a 40% chance that her team wins netball, and a 70% chance that she wins her tennis match. 


What is the probability that she loses both the netball match and the tennis match?


Give your answer as a percentage.

18

%

%

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OR rule


The OR rule is used to find the probability of either of two events happening.


To find the probability of either of two events happening (for example event A OR event B), you just add their individual probabilities together. 


P(A OR B) = P(A) + P(B)

Example:


When rolling a dice, what is the probability of rolling either a 2 or a 3? 

We could write this as:


P(2 OR 3) = P(2) + P(3)


P(2 OR 3) = 1/6 + 1/6 = 2/6 = 1/3


So the probability of rolling a '2', or a '3' is 1/3, or 33.3%.


Note: 


To use the 'OR' rule, the two events must be mutually exclusive. Mutually exclusive means that the two outcomes of the same event cannot happen at the same time. 

When rolling a die, what is the probability of rolling either a 1, 2, or a 3?


Give your answer as a fraction in its simplest form.

\frac{1}{2}

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Jennifer is wondering what to do on the weekend. There is a 1/10 chance that her friends will want to go to the movies, and a 2/5 chance that they will want to go ice skating.


What is the probability that her friends will want to go to the movies or ice skating? 

\frac{1}{2}

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