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?

Expert Answers

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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


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

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