Question

You have a bag of chocolate candy. Ten of them are red, 7 are brown, 12 are green, and 9 are blue. What is the probability that you pick a red candy, given that you have already picked a blue candy and have not replaced it? A) 10 37 B) 14 19 C) 5 19 D) 9 37

Answer 1

You have a total of 38 candies to begin with.  If you pick a blue one and do not replace it, then you'll now have 37.  There are 10 red candies out of 37.  The answer is A.  

Answer 2

Answer: The correct option is (A)
`(10)/(37).`

Step-by-step explanation: Given that in a bag of chocolate candy, ten of them are red, 7 are brown, 12 are green, and 9 are blue.

We are to find the probability that we pick a red candy, given that we have already picked a blue candy and have not replaced it.

We have

Probability of picking a blue candy is given by

`P_b=\frac{\textup{number of blue candies}}{\textup{total number of candies}}\\\\\\\Rightarrow P_b=(9)/(10+7+12+9)\\\\\\\Rightarrow P=(9)/(38).`

Now, since we have already picked a blue candy and did not replace it, so total number of candies left in the bag = 10+7+12+8 = 37.

There are 10 red candies in the bag,

so the probability of picking a red candy given that we have already picked a blue candy and have not replaced it will be

`P_(r/b)=\frac{\textup{number of red candies in the bag}}{\textup{total number of candies left in the bag after picking a blue candy}}\\\\\\\Rightarrow P_(r/b)=(10)/(37).`

Thus, the required probability is
`(10)/(37).`

Option (A) is correct.