1. What are Combined events in probability?
In probability, events occurring at the same time are called combined events. These events can be shown in different ways, such as by systematic listing of all the possible outcomes of the event or by using tables, grids, venn diagrams or tree diagrams.
1.1 Dependent combined events
If the happening of one event affects the probability of happening of another event, such events are called dependent combined events.
For example picking up a green marble then picking up a blue marble without replacing the green marble first. Probability for such events can be worked out using Conditional Probability.
1.2 Independent combined events
If the happening of one event does not affect the probability of happening of another event, such events are called independent combined events.
For example rolling a four both times on two dice rolls, or picking up a green marble, then replacing it and picking up a blue marble. Probability for such events can be worked out using AND rule.
In this article, we will be focusing on working out probabilities of independent events using AND, OR rules.
2. Probability rules
2.1. AND Probability rule
- The AND rule gives the probability of both the events happening together.
- It states that the probability of independent events A and B both happening together is equal to two separate probabilities A and B multiplied together.
- P(A and B) = P(A) + P(B)
Let us now apply the AND rule to work out probability in the example below:
Example: Bag A contains 15 green marbles and 35 yellow marbles, while bag B contains 24 green marbles and 26 yellow marbles. If one marble is picked up at random from each bag, work out the probability of picking green marbles from both the bags.
2.2 OR Probability rule
- When events can’t happen together, they are called mutually exclusive events.
- OR rules gives the probability of two mutually exclusive events.
- It states that the probability of mutually exclusive events A or B happening is equal to two separate probabilities A and B added together.
- P(A or B) = P(A) + P(B)
Let us now apply the OR rule to work out probability in the example below:
Example: A sweet box contains four different types of sweets: toffee, fudge, jelly and mint. A sweet is taken at random from the sweet box. The table below shows the probabilities of taking each type of sweets.
What is the probability that a fudge or a mint is taken from the sweet box?
3. Applying both AND and the OR probability rules
In some questions, you might need to use both AND and OR rule to work out the required probability. Let us see one such example.
Example: Ruby and Antonio each roll a fair six-sided dice. What is the probability that they both roll a number less than 4 or an odd number?
