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A fish tank contains a number of fish, including 5 Fantails. If two fish are selected from the tank at random, what is the probability that both will be Fantails?

Difficulty: 600-700 Level, Probability, Data Sufficiency (DS)

Lunes 25 de julio de 2022, por hurtado claudio

A fish tank contains a number of fish, 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 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


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EXPLANTION:
Statement 1: This choice says that the no. of fish=5, The probability of Fantail=5/10=1/2. Sufficient.

Statement 2:
Let the no. of fish=x,
1.Prob of first (Fish)+ Prob of second (Fantail) Or
2. Prob of both(Fantail)
1.[(x/x+5)]*[(x-1)/(x+5-1)]=4/9.

x is not an integer. (NOT POSSIBLE)

2. This gives x=5.(Only Possible Value).

Therefore the answer is Option D.

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