In a small lake, it is estimated that there are 105 fish, of which 40

Question

In a small lake, it is estimated that there are 105 fish, of which 40 are trout and 65 are carp. A fisherman caught eight fish; what is the probability that exactly two of them are trout if we know that at least three of them are not?

A. 0.239
B. 0.275
C. 0.354
D. 0.375
E. 0.761

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Official Answer

A

A. 0.239
B. 0.275
C. 0.354
D. 0.375
E. 0.761

chiragarora001 · Answer

The fisherman can catch 6 carp and 2 trout in (65C6)(40C2) ways,

hence the probability of catching 6 carp and 2 trout is (65C6)(40C2)/(105C8)

The probability of catching "less" than 3 carp is will be catching 0, 1 or 2 carp.

Then the probability of catching at least 3 carp is 1-P(<3\ carp)

The probability of catching 0 carp is the probability of catching 8 trout, which is (65C0)(40C8)/(105C8)

The probability of catching 1 carp is the probability of catching 1 carp and 7 trout, which is (65C1)(40C7)/(105C8)

The probability of catching 2 carp and 6 trout is (65C2)(40C6)/(105C8)

Therefore, the probability of catching exactly 2 trout given that at least 3 of the 8 fish caught are carp is

(65C6)(40C2)/(105C8)/{1− /(105C8)}

=0.239 approx.

Neder · Answer

Is it possible to calculate it without a calculator? How should you approach this question during the exam?

DmitryFarber · Answer

Simple--you would never see this on the exam.  :cool: The GMAT wouldn't do that to you, but feel free to play with solutions for a challenge.

mumuxi · Answer

assume: 1. if remove 5 carps out of lake and percentage change is small
2. 8 out 100 fish is not going to affect the probably much if we put the fish back (or saying 8/100 ~ 7/99) , 
so changed the question to binomial types:

100 fish, 40 trouts and 60 carp
P(T) = 0.4
P(C) = 0.6
P(T=2) = C(8,2)0.4**2*0.6**6 = 28x0.16x0.22**2 = 0.216
P(>=3 carp) = 1-P(C=0)-P(C=1)-P(C=2)
P(C=0)=0.4**8 v small, drop
P(C=1) = 8*0.4**7x0.6 v small can drop
P(C=2) = C(8,2)0.6**2*0.4**6 = =28x0.36x.16**3 = 0.04
so P(T=2) / (1-P(>=3 carp) ) = 0.216/(1-0.04) = 0.225

A

In a small lake, it is estimated that there are 105 fish, of which 40

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In a small lake, it is estimated that there are 105 fish, of which 40

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

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