There is 1 red gumdrop and 4 green gumdrops in a small jar. Also, there are 2 pieces of butterscotch candy and 3 pieces of cinnamon candy in another jar. If Craig draws one piece of candy from each jar without looking, what's the probability that he will get a red gumdrop and a piece of butterscotch candy?
A. [tex]\frac{4}{25}[/tex] B. [tex]\frac{3}{25}[/tex] C. [tex]\frac{3}{10}[/tex] D. [tex]\frac{2}{25}[/tex]
To solve for the probability that Craig will draw a red gumdrop from the first jar and a piece of butterscotch candy from the second jar, follow these steps:
1. Determine the probability of drawing a red gumdrop from the first jar: - Total number of gumdrops in the first jar = 1 red + 4 green = 5 gumdrops. - Number of red gumdrops = 1. - Probability of drawing a red gumdrop = Number of red gumdrops / Total number of gumdrops = [tex]\( \frac{1}{5} \)[/tex].
2. Determine the probability of drawing a butterscotch candy from the second jar: - Total number of candies in the second jar = 2 butterscotch + 3 cinnamon = 5 candies. - Number of butterscotch candies = 2. - Probability of drawing a butterscotch candy = Number of butterscotch candies / Total number of candies = [tex]\( \frac{2}{5} \)[/tex].
3. Calculate the probability of both events happening: - The events of drawing a red gumdrop from the first jar and drawing a butterscotch candy from the second jar are independent events. - The combined probability of both independent events happening is the product of their individual probabilities. - Probability = [tex]\( \frac{1}{5} \)[/tex] (probability of red gumdrop) [tex]\(\times \frac{2}{5} \)[/tex] (probability of butterscotch candy) = [tex]\(\frac{1 \times 2}{5 \times 5} = \frac{2}{25}\)[/tex].
Thus, the probability that Craig will draw a red gumdrop and a piece of butterscotch candy is [tex]\( \frac{2}{25} \)[/tex].
The correct answer is: D. [tex]\( \frac{2}{25} \)[/tex]
