SOLUTION: A sack filled with marbles contains: 17 red marbles numbered 1 to 17 35 blue marbles numbered 1 to 35 42 green marbles numbered 1 to 42 13 yellow marbles numbered 1 to 13 T

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Question 1202743: A sack filled with marbles contains:
17 red marbles numbered 1 to 17
35 blue marbles numbered 1 to 35
42 green marbles numbered 1 to 42
13 yellow marbles numbered 1 to 13
The answer should be entered as a decimal and if necessary, round to at least four decimal places.
If you randomly pull one marble out of the sack, set it aside, then pull a second marble, what is the probability of drawing a yellow marble followed by a green marble?

Answer by math_tutor2020(3838) (Show Source):
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The numbers on the marbles appear to be a distraction.

A = marble is yellow on 1st selection
B = marble is green on 2nd selection

P(A) = (13 yellow)/(17+35+42+13 total)
P(A) = 13/107

P(B given A) = probability B happens given we know A happened
P(B given A) = (42 green)/(107-1 remaining)
P(B given A) = 42/106
P(B given A) = 21/53

P(A and B) = P(A)*P(B given A)
P(A and B) = (13/107)*(21/53)
P(A and B) = 0.04813965790866
P(A and B) = 0.0481

Answer: 0.0481 (approximate)