SOLUTION: A child has three bags of fruits in which Bag 1 has 5 apples and 3 oranges, Bag 2 has 4 apples and 5 oranges and Bag 3 has 2 apples and 3 oranges. One fruit is drawn at random from

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Question 1196063: A child has three bags of fruits in which Bag 1 has 5 apples and 3 oranges, Bag 2 has 4 apples and 5 oranges and Bag 3 has 2 apples and 3 oranges. One fruit is drawn at random from one of the bags. It was an apple. Please calculate the probability that the chosen fruit was apple and was drawn from Bag 3.
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3816)   (Show Source): You can put this solution on YOUR website!

Edit: Corrected an earlier mistake.

Bag 1 has 5 apples and 3 oranges
Bag 2 has 4 apples and 5 oranges
Bag 3 has 2 apples and 3 oranges

We're given this info:
One fruit is drawn at random from one of the bags. It was an apple.
So we know 100% that the fruit was an apple. The only thing to figure out is the probability it came from bag 3.

There are
5 apples in bag 1
4 apples in bag 2
2 apples in bag 3
That's 5+4+2 = 11 apples total

This is our sample space. It's our entire universe because we know 100% we picked an apple. So we ignore the oranges entirely.

Of the 11 apples in the universal set, 2 are from bag 3

Answer: 2/11
Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
.
A child has three bags of fruits in which
Bag 1 has 5 apples and 3 oranges, Bag 2 has 4 apples and 5 oranges and Bag 3 has 2 apples and 3 oranges.
One fruit is drawn at random from one of the bags. It was an apple.
Please calculate the probability that the chosen fruit was apple and was drawn from Bag 3.
~~~~~~~~~~~~~~~~~~~ 

Total fruit in 3 bags  was (5+3) + (4+5) + (2+3) = 22.

Total apples in 3 bags was  5 + 4 + 2 = 11.


The probability that the drawn fruit was an apple is   =  = 0.5 = 50%.    ANSWER


If it is given that the drawn fruit is an apple, 
then the probability that the drawn apple came from bag 3 is  .     ANSWER

Solved.



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