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11 Jul 2017, 03:22
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D
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Difficulty:
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Question Stats:
80% (01:16) correct
20%
(01:20)
wrong
based on 265
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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?
(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
ORIGINAL VERSION:
(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
ORIGINAL VERSION:
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) The probability that the second fish chosen will be a Fantail is 4/9.
Edited because of the reasons sited by IanStewart HERE.
(1) The probability that the first fish chosen will be a Fantail is 1/2.
(2) The probability that the second fish chosen will be a Fantail is 4/9.
Edited because of the reasons sited by IanStewart HERE.
11 Jul 2017, 04:05
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Bunuel
Assume that that fish tank contains 5 Fantails and \(n\) other fishes. The total fishes in that tank are \(n+5\)
A is the case that the first fish chosen will be a Fantail
B is the case that the second fish chosen will be a Fantail
(1) We have \(P(A) = \frac{5}{n+5}=\frac{1}{2} \implies n=5\). Since we know how many fishes are in that fish tank, we will know the probability to select 2 Fantails from that tank. Sufficient.
(2) Note that the probability that the second fish chosen is based on the first fish selected. Hence we have
\(P(B|A)=\frac{4}{n+4} = \frac{4}{9} \implies n=5\). Sufficient.
The answer is D
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) The probability that the second fish chosen will be a Fantail is 4/9.
Solution:
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.
Solving this, we get x^2-9x-16=0.
x is not an integer.(NOT POSSIBLE)
2. This gives x=5.(Only Possible Value).
Therefore the answer is Option D.
Correct me if I am wrong.
(1) The probability that the first fish chosen will be a Fantail is 1/2.
(2) The probability that the second fish chosen will be a Fantail is 4/9.
Solution:
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.
Solving this, we get x^2-9x-16=0.
x is not an integer.(NOT POSSIBLE)
2. This gives x=5.(Only Possible Value).
Therefore the answer is Option D.
Correct me if I am wrong.
