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Independent and Dependent Events, a la Shmoop. Congratulations! You've been chosen as a contestant

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on that game show where people dress up in silly costumes and try to win prizes.

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You're dressed as Euclid, but the host keeps calling you Gandalf. Go figure.

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To win the car, you have to spin this spinner... And meet two conditions:

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One. You have to spin an odd number on the first spin.

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Two: The sum of the two numbers you spin must be odd.

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This is a little more complicated than Plinko... We want to know if, using the formal definition

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of independenceÉ É events A and B are independent or dependent.

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Before we start, lets define what makes an event independent or dependentÉ

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A dependent event depends on the outcome of a secondary eventÉ

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Éwhile an independent event doesnÕt have to answer to anybody. HeÕs more of a free spirit.

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As the audience cheers you on, let's give this problem a spin.

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Here's a chart of the possible outcomes. The numbers down the side show up on the first

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spin; the numbers across the top show up on the second spin.

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The numbers in the table show the sum of the two spins.

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Nowhere in there is your new car. Don't get your hopes up.

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Since both one and three are odd, the probability of getting an odd number on your first spin

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is good. The probability of A is two out of three.

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It's a little more difficult to spin twice and still have an odd number.

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Since there are 9 total possible outcomes and 4 of them are oddÉ

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The probability of B on its own is four out of nine.

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But remember, the only results that count are the ones that occur when you spin an odd

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number first. The probability of A and B happeningÉ the

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only outcomes that occur in both tablesÉ is two out of nine.

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They don't make these things easy. Maybe you should just take what's behind curtain number

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two. But what we really want to know is if these

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events are independent or dependent. Since the probability of A, two-thirds, times

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the probability of B, four-ninths, which comes out to eight-twenty-sevenths, does NOT equal

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the probability of A and B, which is two-ninths, the events are dependent.

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We can't give you a car, but we can help give you a better grade.

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Which is even better, really. At least with a better grade, you donÕt have to make monthly

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payments.

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