One urn contains 8 blue balls and 12 white balls, and a second urn contains 14 blue balls and 5 white balls. an urn is selected at random, and a ball is chosen from the urn. (round your answers to one decimal place.) (a) what is the probability (as a %) that the chosen ball is blue? (b) if the chosen ball is blue, what is the probability (as a %) that it came from the first urn? need ? read it talk to a tutor

a) The probability that the chosen ball is blue is 56.84%

b) If the chosen ball is blue, there is a 35.19 probability that it came from the first urn.

Step-by-step explanation:

a) What is the probability (as a %) that the chosen ball is blue?

First the urn is chosen, then the ball. There can be a blue ball from urn 1 and from urn 2.

-The probability of a blue ball being chosen from urn 1 is:

40%(8 blue balls among 20 in urn 1, 8 of 20 is 40%) of 50%(the chance of urn 1 being chosen is 50%)

So

-The probability of a blue ball being chosen from urn 2 is:

73.68%(14 blue balls among 20 in urn 2, 14 of 19 is 73.68%) of 50%(the chance of urn 2 being chosen is 50%)

So

The probability that the chosen ball is blue is %.

b) If the chosen ball is blue, what is the probability (as a %) that it came from the first urn?

This item can be formulated as the following problem:

What is the probability of B happening, knowing that A has happened.

It can be calculated by the following formula

Where P(B) is the probability of B happening, P(A/B) is the probability of A happening knowing that B happened and P(A) is the probability of A happening.

In this item, A(what has happened) is the ball being blue. In item a), we found that P(A) = 0.5684.

B is the blue ball coming from the first urn. P(B), the probability of the first urn being chosen, is 50% = 0.5.

P(A/B), the probability of the blue ball being chosen from the first urn is 40% = 0.4.

So:

If the chosen ball is blue, there is a 35.19 probability that it came from the first urn.

the answer is c)8

step-by-step explanaction:

answer: all of the odd numbers were opened

the first person was the one that was opening all of the lockers. since one is odd, this causes all of the odd number lockers to be opened in the end.