SOLUTION: A bag contains 4 red chips and 4 blue chips. Another bag contains 2 red chips and 6 blue chips. A chip is randomly selected from one of the bags, and found to be blue. What is the

Question 1172381: A bag contains 4 red chips and 4 blue chips. Another bag contains 2 red chips and 6 blue chips. A chip is randomly selected from one of the bags, and found to be blue. What is the probability that the chip is from the first bag?
Answer by math_tutor2020(3816) (Show Source): You can put this solution on YOUR website!

Quick Method:
Ignore the red chips since we know the chip is blue.

We have 4 blue chips in bag A and 6 blue chips in bag B. There are 4+6 = 10 blue chips total.

The probability the blue chip is from bag A is 4/10 = 2/5, which is the answer.

-----------------------------------------------------
A more in-depth look:

Use the law of total probability to say that
P(blue) = P(blue and bag A) + P(blue and bag B)
P(blue) = P(blue, given bag A)*P(bag A) + P(blue, given bag B)*P(bag B)
P(blue) = (4/8)*(1/2) + (6/8)*(1/2)
P(blue) = (4/8+6/8)*(1/2)
P(blue) = (10/8)*(1/2)
P(blue) = 10/16
P(blue) = 5/8

Now use conditional probability
P(blue, given bag A) = P(bag A and blue)/P(bag A)
P(blue, given bag A)*P(bag A) = P(bag A and blue)
P(bag A and blue) = P(blue, given bag A)*P(bag A)

P(bag A, given blue) = P(bag A and blue)/P(blue)
P(bag A, given blue) = P(blue, given bag A)*P(bag A)/P(blue)
P(bag A, given blue) = (1/2)*(1/2)/(5/8)
P(bag A, given blue) = (1/4)/(5/8)
P(bag A, given blue) = (1/4)*(8/5)
P(bag A, given blue) = 8/20
P(bag A, given blue) = 2/5

If we know the chip is blue, the probability of it being from bag A is 2/5.

=====================================================

Answer: 2/5

RELATED QUESTIONS
A bag contains 6 red chips, 9 white chips, and 5 blue chips. Three consecutive chips are... (answered by checkley75)

A bowl contains 5 red chips 7 blue chips 6 yellow chips and 20 green chips . One chip is... (answered by ewatrrr)

A bag contains 7 red chips and 10 blue chips. Two chips are selected randomly without... (answered by jim_thompson5910)

A bag contains five red chips, three white chips, and two blue chips. Three chips are to... (answered by ewatrrr)

a bag contains 5 red chips, 3 white chips, and 2 blue chips. 3 chips are to be selected... (answered by stanbon)

a bag contains 5 red chips, 3 white chips, and 2 blue chips. three chips are selected... (answered by stanbon)

A bowl contains 4 red chips, 3 blue chips, and 9 green chips. You choose one chip at... (answered by ewatrrr)

a box has 2 red chips, 2 blue chips. and 1 green chip. 2 chips are randomly selected... (answered by chiggypiggy)

a box contains 8 red chips, 6 blue chips, and 12 white chips. three chips are randomly... (answered by stanbon)