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Determine whether the following individual events are independent or dependent. Then find the probability of the combined event.
Randomly drawing and immediately eating two red pieces of candy in a row from a bag that contains 10 red pieces of candy out of 51 pieces
of candy total.
=
Choose the correct answer below.
(Round to three decimal places as needed.)

A. The individual events are dependent. The probability of the combined event is_____?

Or

B. The individual events are independent. The probability of the combined event is _____?
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Answer 1

Explanation:

A. The individual events are dependent. The probability of the combined event is:

The probability of drawing a red piece of candy on the first draw is 10/51. Since we do not replace the candy after the first draw, the probability of drawing another red piece of candy on the second draw depends on what happened on the first draw. If a red piece of candy was drawn on the first draw, then there are 9 red pieces of candy left out of 50 total pieces of candy for the second draw. If a non-red piece of candy was drawn on the first draw, then there are still 10 red pieces of candy left out of 50 total pieces of candy for the second draw. Therefore, the probability of drawing two red pieces of candy in a row is:

(10/51) x (9/50) + (41/51) x (10/50) = 0.0698

Rounded to three decimal places, the probability of the combined event is 0.070.