A probability describes how likely it is that an event may occur. You’ll see probabilities represented as percentages from 0% to 100%, which correspond to their decimal values from 0 to 1.
Since something will either happen or it won’t, the sum of these two probabilities will always add up to , i.e. a chance. For example, imagine we’re picking a marble from a bag, and there’s a chance it will be blue. What is the probability it won’t be blue? That probability is .
A probability can be found by dividing the number of desired outcomes by the number of total possible outcomes. For example, if you and your brother are participating in a raffle, and you both would be happy with either of you winning, and there are 20 total people participating in the raffle, the chance of winning the raffle is 2/20 = .1 or 10%. There are two desired tickets to be drawn and 20 total tickets possible.
There are two rules that can be helpful when working with probabilities: AND and OR.
Let’s think about this question for a moment:
What is the chance of winning a coin flip twice in a row?
Coin flips are luck-based, and the chance of winning a single coin flip is , represented in decimal form as . Because we are trying to win twice in a row (i.e. winning the first flip and the second flip), this is an AND situation.
The probability of winning twice in a row is .
Let’s try another example.
You are tasked with randomly selecting criminals from a police lineup. There are two accomplices in the crime. What is the chance you overlook both criminals when randomly selecting two from a lineup that includes 7 suspects? Express the probability in terms of a fraction.
Try to solve it yourself, then check below!
Answer:
This question asks for the probability of selecting a non-criminal and then selecting a second non-criminal, so we have to multiply the two probabilities together.
There are criminals, so given our group has suspects, there must be non-criminals. The probability of selecting a non-criminal for the first pick is . After making this choice that one non-criminal is no longer in the lineup, so the chance of selecting a second non-criminal is .
Think about this question:
What is the chance of randomly selecting a consonant or the letter A from the alphabet?
There are 21 consonants in the alphabet and obviously, there is a single letter A. Because this is an OR situation, you should add the probabilities. There is a chance of selecting a consonant and a chance of selecting the letter A. The total probability of selecting either a consonant or A is:
Divided out, is approximately .
Let’s try another example.
Probabilities , , and are the chances of three mutually exclusive events occurring. No other possible events can occur beyond these three events.
Quantity A: The chance that or occurs
Quantity B:
Give it a try!
Answer: C. The quantities are equal
The probability that or could occur is equivalent to .
In Quantity B, the represents all possible outcomes, i.e., there is a 100% chance that one of the three mutually exclusive events occurs. This can be represented as the equation , which we can rearrange to get Quantity B’s value of .
So, it turns out that both Quantity A and Quantity B are .
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