A jar of 70 candies has the following colors: 28 orange, 7 white, 14 brown, and 21 yellow.
What is the probability of randomly drawing a candy that is not brown, replacing it, and then drawing a white candy?
There are a total of 70 candies in the jar.
To calculate the probability of drawing a candy that is not brown and replacing it, we need to find the number of candies that are not brown.
The number of candies that are not brown = total number of candies - number of brown candies
= 70 - 14
= 56 candies
Since we are replacing the candy after each draw, the probability of drawing a candy that is not brown is:
Probability of drawing a candy that is not brown = (number of candies that are not brown) / (total number of candies)
= 56 / 70
= 0.8 or 80%
Next, we need to calculate the probability of drawing a white candy from the 70 candies (after replacing the candy drawn in the first step).
The number of white candies in the jar = 7
The probability of drawing a white candy = (number of white candies) / (total number of candies)
= 7 / 70
= 0.1 or 10%
Therefore, the probability of randomly drawing a candy that is not brown, replacing it, and then drawing a white candy is:
Probability = (probability of drawing a candy that is not brown) * (probability of drawing a white candy)
= 0.8 * 0.1
= 0.08 or 8%
To find the probability of drawing a candy that is not brown, replacing it, and then drawing a white candy, we need to calculate the individual probabilities of each event and multiply them together.
First, let's calculate the probability of drawing a candy that is not brown:
Total number of candies = 70
Number of candies that are not brown = 70 - 14 = 56
Probability of drawing a candy that is not brown = (Number of candies that are not brown) / (Total number of candies) = 56/70 = 4/5
Since we are replacing the candy after the first draw, the number of candies remains the same for the second draw. Therefore, the probability of drawing a white candy is still the same.
Number of white candies = 7
Total number of candies = 70
Probability of drawing a white candy = (Number of white candies) / (Total number of candies) = 7/70 = 1/10
Now, let's calculate the probability of both events happening together (drawing a candy that is not brown and then drawing a white candy):
Probability of not drawing a brown candy and then drawing a white candy = (Probability of not drawing a brown candy) * (Probability of drawing a white candy)
Probability of not drawing a brown candy and then drawing a white candy = (4/5) * (1/10) = (4/50) = 0.08
So, the probability of randomly drawing a candy that is not brown, replacing it, and then drawing a white candy is 0.08 or 8%.