Angie and Eric have opened a jumbo bag of candies and counted the number of each color. They have 100 red, 180 green, 90 yellow, and 130 brown candies. Sarah and Laney each take turns drawing a candy, replacing each candy after they draw. If Angie and Eric each draw a candy 500 times, how many times should they expect for Angie to draw a brown candy followed by Eric drawing a red candy?

Question

Mathematics

Zachariah

5 November, 23:46

Angie and Eric have opened a jumbo bag of candies and counted the number of each color. They have 100 red, 180 green, 90 yellow, and 130 brown candies. Sarah and Laney each take turns drawing a candy, replacing each candy after they draw. If Angie and Eric each draw a candy 500 times, how many times should they expect for Angie to draw a brown candy followed by Eric drawing a red candy?

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Answers (1)

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Allisson Bright · Answer 1

26 times.

Step-by-step explanation:

Total number of candies = 500.

Probability (Angie drawing a brown candy) = 130/500 = 13/50.

Probability (Eric drawing a red candy) = 100/500 = 1/5.

So Probability (Angie drawing brown then Eric drawing a red) = 13/50 * 1/5

= 13/250.

Therefore the expectation of the number of times this will happen

= Probability * total number of draws

= (13/250) * 500

= 13 * 2

= 26 times.