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Joint Entrance Examination
Mathematics
Probability
Question 219
Question 219 of 417
Medium
MCQ
An urn contains 5 red, 2 green balls. A ball drawn; if green, a red ball is added; if red, a green ball is added (original not returned). A second ball is drawn. Find the probability the second ball is red.
A
21
/
49
21/49
21/49
B
27
/
49
27/49
27/49
C
26
/
49
26/49
26/49
D
32
/
49
32/49
32/49
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Official solution
\[P(\text{2nd red}) = P(G)\cdot P(R\mid G)+P(R)\cdot P(R\mid R) = \frac27\times\frac67+\frac57\times\frac47 = \frac{12+20}{49}=\frac{32}{49}\]
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