if you have a bag of chocolate candy, ten are red, 7 are brown, 12 are green, and 9 are blue, what is the probability of you picking a red candy given that you already picked a blue candy and have not replaced it?
the actual answer is 9/37
10 + 7 + 12 + 8 = 37
10/37 = 0.27 = 27%
10/37
To calculate the probability of picking a red candy given that you already picked a blue candy and have not replaced it, we need to determine the number of red candies remaining in the bag after picking a blue candy.
First, let's calculate the total number of candies before picking any:
Total number of candies = number of red candies + number of brown candies + number of green candies + number of blue candies
Total number of candies = 10 + 7 + 12 + 9 = 38
Now, since you have already picked a blue candy and did not replace it, the total number of candies in the bag is reduced by one:
Total number of candies remaining = Total number of candies - 1
Total number of candies remaining = 38 - 1 = 37
Next, let's calculate the total number of red candies remaining:
Total number of red candies remaining = Total number of red candies - 1
Total number of red candies remaining = 10 - 1 = 9
Finally, we can calculate the probability of picking a red candy given the conditions:
Probability of picking a red candy = Number of red candies remaining / Total number of candies remaining
Probability of picking a red candy = 9 / 37 ≈ 0.243 or 24.3%
Therefore, the probability of picking a red candy given that you already picked a blue candy and have not replaced it is approximately 24.3%.