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An experiment consists of drawing a marble out of a bag, observing the color, and then...

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Elprimito89 | eNotes Newbie

Posted October 21, 2013 at 5:09 PM via web

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An experiment consists of drawing a marble out of a bag, observing the color, and then placing it back in the bag. Suppose the experiment is repeated 75 times, with the following results:
red         38
blue        23
green      11
yellow      3
What is the probability of drawing two yellow marbles in a row?

Tagged with math, probability

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tiburtius | High School Teacher | (Level 3) Associate Educator

Posted October 21, 2013 at 5:39 PM (Answer #1)

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Those numbers actually represent frequencies of the drawing the balls. We can approximate relative frequencies with probabilities of drawing each of the balls.

So probability of drawing a red ball would be `38/75` because red ball was drawn 38 out of 75 times. Analogously we obtain probabilities of drawing other balls: blue `23/75,` green `11/75` and yellow `3/75=1/25.`

Now probability of drawing two yellow in a row. Since we put a marble back each time it follows that the drawings are mutually independent and probability of two independent events happening is equal to product of their respective probabilities. Thus we have

`1/25cdot1/25=1/625=0.0016`    

So probability of drawing two yellow balls in a row is `1/625.`

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Elprimito89 | eNotes Newbie

Posted October 21, 2013 at 5:43 PM (Answer #2)

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A pizza shop has 18 different toppings to choose from.  Today?s special comes with a choice of 5 toppings, plus a choice of 3 types of crust: thin crust, regular, and deep dish crust.

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