Independent and Dependent Events, a la Shmoop.
Congratulations!
You've been chosen as a contestant on that game show where people dress up in silly costumes
and try to win prizes.
You're dressed as Euclid, but the host keeps calling you Gandalf.
Go figure.
To win the car, you have to spin this spinner...
And meet two conditions: One.
You have to spin an odd number on the first spin.
Two: The sum of the two numbers you spin must be odd.
This is a little more complicated than Plinko...
We want to know if, using the formal definition of independenceÉ
É events A and B are independent or dependent.
Before we start, lets define what makes an event independent or dependentÉ
A dependent event depends on the outcome of a secondary eventÉ
Éwhile an independent event doesnÕt have to answer
to anybody.
HeÕs more of a free spirit.
As the audience cheers you on, let's give this problem a spin.
Here's a chart of the possible outcomes.
The numbers down the side show up on the first spin; the numbers across the top show up on
the second spin.
The numbers in the table show the sum of the two spins.
Nowhere in there is your new car.
Don't get your hopes up.
Since both one and three are odd, the probability of getting an odd number on your first spin
is good.
The probability of A is two out of three.
It's a little more difficult to spin twice and still
have an odd number.
Since there are 9 total possible outcomes and 4 of them are oddÉ
The probability of B on its own is four out of nine.
But remember, the only results that count are the ones that occur when you spin an odd
number first.
The probability of A and B happeningÉ the only outcomes that occur in both tablesÉ
is two out of nine.
They don't make these things easy.
Maybe you should just take what's behind curtain number two.
But what we really want to know is if these events are independent or dependent.
Since the probability of A, two-thirds, times the probability of B, four-ninths, which comes
out to eight-twenty-sevenths, does NOT equal the probability of A and B, which is two-ninths,
the events are dependent.
We can't give you a car, but we can help give you a better grade.
Which is even better, really.
At least with a better grade, you donÕt have to make monthly payments.