An experiment consists of drawing two marbles from an earn without replacement. There are 7 red marbles and 5 blue marbles in the urn. Let the events be defined as follows: R1 = Drawing a red marble on the first draw. R2 = Drawing a red marble on the second draw. B1 = Drawing a blue marble on the first draw. B2 = Drawing a blue marble on the second draw. What is P(B1)? /
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Step-by-step explanation:
There is 5 blue marbles and 7 green marbles. Two are drawn in succession without replacement. What is the probability that the first drawn is a green, given that the second marble drawn is blue?
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Jonathan Fivelsdal
Answered May 17, 2018 · Author has 444 answers and 580.1K answer views
First define the following events A and B:
A: The first marble is green
B: The second marble is blue
The probability of interest is the conditional probability P(A∣B)P(A∣B).
The formula for P(A∣B)P(A∣B) is the following:
P(A∣B)=P(A∩B)P(B)P(A∣B)=P(A∩B)P(B).
The probability P(A∩B)P(A∩B) is the probability that the first marble is green and the second marble is blue. The probability of the intersection of A and B is
P(A∩B)=712511P(A∩B)=712511
=35132=35132.
Now find the probability that the second marble is blue (this is P(B)P(B) ).
Note that P(B)=P(A∩B)+P(AC∩B)P(B)=P(A∩B)+P(AC∩B), where ACAC is the complement of the event A (in this problem the complement of A is that the first marble is blue). Observe the following:
P(B)=P(A∩B)+P(AC∩B)P(B)=P(A∩B)+P(AC∩B)
=712511+512411=712511+512411