What are Equally Likely Outcomes?
Equally likely outcomes are, like the name suggests, events with an equal chance of happening. Many events have equally likely outcomes, like tossing a coin (50% probability of heads; 50% probability of tails) or a die (1/6 probability of getting any number on the die).
In real life though, it’s highly unusual to get equally likely outcomes for events. For example, the probability of finding a golden ticket in a chocolate bar might be 5%, but this doesn’t contradict the idea of equally likely outcomes. Let’s say there are 100 chocolate bars and five of them have golden ticket, which gives us our 5% probability. Each of those golden tickets represents one chance to win, and there are five chances to win, each of which are equally likely outcomes. Other examples:
- Flip a fair coin 10 times to see how many heads or tails you get. Each event (getting a heads or getting a tails) is equally likely).
- Roll a die 3 times and note the sequence of numbers. Each sequence of numbers (123,234,456,…) is equally likely.
How to Find the Probability of Equally Likely Outcomes
Formally, equally likely outcomes are defined as follows:
For any sample space with N equally likely outcomes, we assign the probability 1/N to each outcome.[1]
To find the probability of equally likely outcomes:
- Define the sample space for an event of chance. The sample space is all distinct outcomes. For example, if 100 lottery tickets are sold numbered 1 through 100, the sample space is a list of all winning tickets (1, 2, 3, …, 100).
- Count the number of ways event A can occur. For this example, let’s say that event A is “picking the number 33”. There is only one way to choose the number 33 from the list of numbers 1 through 100.
- Divide your answer from (2) by your answer from (1), giving: 1/100 or 1%.
A slightly more complicated example. Let’s say you were interested in calculating the probability of choosing any ticket with the number three.
- The sample space is still a list of all winning tickets (1, 2, 3, …, 100).
- Event A, “picking a ticket with the number 3”, has ten possibilities: 3, 13, 23, 33, 43, 53, 63, 73, 83, 93.
- Divide your answer from (2) by your answer from (1), giving: 10/100 = 10%.
References
[1] Equally Likely outcomes. Retrieved February 19, 2021 from:
https://www3.nd.edu/~dgalvin1/10120/10120_S16/Topic09_7p2_Galvin.pdf