Suppose you have 3 jars with the following contents. jar 1 has 1 white ball and 4 black balls. jar 2 has 2 white balls and 1 black ball. jar 3 has 3 white balls and 2 black balls. one jar is to be selected, and then 1 ball is to be drawn from the selected jar. the probabilities of selecting the first, second, and third jars are 1/2, 1/3, and 1/6 respectively. find the probability the ball was drawn from jar 1, given that the ball is white.

The probability is:

We need to use the Baye's theorem in order to find the probability .

Jar 1:  has 1 white ball and 4 black balls.

This means that the probability of white ball is: 1/5

( since there are a total of 1+4=5 balls out of which 1 is white)

Jar 2: has 2 white balls and 1 black ball.

This means that the probability of white ball is: 2/3

( since there are a total of 2+1=3 balls out of which 2 are white)

Jar 3 : has 3 white balls and 2 black balls.

This means that the probability of white ball is: 3/5

( since there are a total of 3+2=5 balls out of which 3 are white)

Hence, the probability the ball was drawn from Jar 1, given that the ball is white is:

Ratio of drawing jar 1 and a white ball from it to the sum of choosing each jar and a white ball from it.

i.e.

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