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?

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:...

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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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