Probability
"Tell the Future"
It may not be possible to tell the future, but probability can describe the likelihood of an event coming to pass. The song explains the different ways of expressing probability, as a decimal, percentage or fraction between zero and one. It also walks students through calculating probability using the common examples of a coin flip and a dice toss.
Yeah, everybody wants to tell the future. What if you could use math to do it though?
I can’t tell the future, but I can try,
Using odds and probability as my guide. Right?
That describes what would be the chances,
Of an event coming to pass.
'Cause I can't just tell the future, but I can try,
Using odds and probability as my guide. Right?
That describes what would be the chances,
Of an event coming to pass, 'cause I can't just...
Tell the future, nope, never,
But odds and probability make it better.
Take any number between 0 and 1,
And this relates to the expected outcome.
0? Not even a chance,
Like Sunday coming right after Monday and,
1 means it'll happen every single time,
Probability 100% I'm not lying.
So yes, you can express probable action,
As a decimal, percentage or as a fraction.
1⁄5, probably not gonna occur,
That’s .2 or a 20% chance, ya heard?
If I flip a coin, what's the probability
Of getting tails? Well, that’s .5, you feeling me?
Tails is one outcome out of two,
So 50% no matter how many flips you do.
I can’t tell the future, but I can try,
Using odds and probability as my guide. Right?
That describes what would be the chances,
Of an event coming to pass.
'Cause I can't just tell the future, but I can try,
Using odds and probability as my guide. Right?
That describes what would be the chances,
Of an event coming to pass, 'cause I can't just...
Tell the future, but just to have fun,
I can find the likelihood of a specific outcome.
See you figure out how many possibilities there are,
Then you pick which outcome that you're looking for.
Divide the one you want by the total number possible,
Once you get this far, you're unstoppable.
Well how 'bout I let a die fall to the floor,
What’s the chance it could be a 3 or a 4?
2 outcomes out of 6 total, see?
Thats a 33% chance it’s one of these.
Capisce? But that’s just for a single roll,
A compound event is when we roll a few more.
Now with compound events, it’s all right,
Just take each probability and then multiply.
What's the chance I'll roll two 6s in row?
1⁄6 · 1⁄6 = 1⁄36, oh!
I can’t tell the future, but I can try,
Using odds and probability as my guide. Right?
That describes what would be the chances,
Of an event coming to pass.
'Cause I can't just tell the future, but I can try,
Using odds and probability as my guide. Right?
That describes what would be the chances,
Of an event coming to pass, 'cause I can't just...
Probability measures the likelihood that a particular event will occur. You may not be able to tell the future, but you can use probability to make educated guesses about what will happen.
Probability is represented with numbers between 0 and 1. If the probability of something is 0, it means there is absolutely no chance of it happening. If it’s 1, it will definitely happen. If it’s 0.5, that means there is a equal chance of it occurring or not occurring.
Probability can be expressed as either a decimal, a percentage or a fraction. But no matter what form it takes, it means the same thing. 1⁄10, 0.1, and 10% are all equivalent--they’re just different ways of expressing the same probability.
An easy way to convert a percentage to a fraction is to put the number of the percentage over 100 and then simplify: for example, 75% is the same as 75⁄100, or 3⁄4. The first two places after a decimal point are the same as a percentage: 0.15 is equal to 15%, and 0.3 is equal to 30%.
An easy way to convert a percentage to a fraction is to put the number of the percentage over 100 and then simplify: for example, 75% is the same as 75⁄100, or 3⁄4. The first two places after a decimal point are the same as a percentage: 0.15 is equal to 15%, and 0.3 is equal to 30%.
Problems involving coin tosses are very common in probability. Coins always have an equal chance of landing heads or tails. Whether on the first flip or the fifteenth, it will always be a 50% chance for either side.
When coming up with the probability of an outcome, divide the outcome you're looking for by the total number of possible outcomes. In a coin toss, the probability of either side is 1⁄2, as there are two total outcomes. With dice, which have six sides, the probability of one of the numbers landing on top is 1 divided by 6, or 1⁄6.
If you are measuring the probability of rolling either a three or a four, you are measuring for two possible outcomes. You then divide that number by the total number of possible outcomes. Dice have six sides, so you divide two by six.
2⁄6 = 1⁄3.
2⁄6 = 1⁄3.
A compound event involves measuring the probability of more than one event in a row. In order to find that probability, you have to multiply the probabilities of each of the single events together. That product is the probability of the compound event.
For example, if you want to know the likelihood of flipping a coin four times in a row and getting heads every time, you have to multiply the probabilities for each of the four coin flips.
1⁄2 · 1⁄2 · 1⁄2 · 1⁄2 = 1⁄16
That means there is a 1 in 16 chance of getting heads in four coin tosses in a row.
For example, if you want to know the likelihood of flipping a coin four times in a row and getting heads every time, you have to multiply the probabilities for each of the four coin flips.
1⁄2 · 1⁄2 · 1⁄2 · 1⁄2 = 1⁄16
That means there is a 1 in 16 chance of getting heads in four coin tosses in a row.
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