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A fish tank contains a number of fishes, including 5 Fantail

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A fish tank contains a number of fishes, including 5 Fantail

by M7MBA » Sat Nov 30, 2019 4:31 am
A fish tank contains a number of fishes, including 5 Fantails. If two fish are selected from the tank at random, what is the probability that both will be Fantails?

(1) The probability that the first fish have chosen will be a Fantail is 1/2.

(2) If the first selected fish is a Fantail, then the probability the second selection is also a Fantail is 4/9.

[spoiler]OA=D[/spoiler]

Source: Princeton Review
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Source: — Data Sufficiency |
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by deloitte247 » Sun Dec 08, 2019 9:13 am
Fantails = 5
Let other fish = 5
The total fish in the tank = 5 + x
So, if two fishes are selected from the tank at random, what is the probability that both will be Fantails?
Statement 1: The probability that the first fish chosen will be a Fantail is 1/2.
The probability that the first fish chosen will be a Fantail =
$$\frac{5}{5+x}=\frac{1}{2}$$
$$10=5+x$$
$$x=5$$
Therefore, the probability that the second fish chosen will be a Fantail
$$=\frac{4}{4+x},\ where\ x=5$$
$$=\frac{4}{4+5}=\frac{4}{9}$$
Statement 1 is SUFFICIENT.

Statement 2: If the first selected fish is a Fantail, then the probability that the second selection is also a fantail is 4/9.
$$Therefore,\ \frac{4}{4+x}=\frac{4}{9}$$
$$36=4\left(4+x\right)$$
$$36=16+4x$$
$$4x=20$$
$$x=\frac{20}{4}=5$$
And the probability that the two fishes selected are Fantail = 4/9. Hence, statement 2 is also SUFFICIENT.

Conclusively, since each statement alone is SUFFICIENT, then, the correct answer is option B.
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