A scientific research study examined a large number of young foxes

Question

A scientific research study examined a large number of young foxes, that is, foxes between 1 year and 2 years old. The study found that 80% of the young foxes caught a rabbit at least once, and 60% caught a songbird at least once If 10% of the young foxes never caught either a rabbit or a songbird, then what percentage of young foxes were successful in catching at least one rabbit and at least one songbird?

A. 40%
B. 50%
C. 60%
D. 80%
E. 90%

Kudos for a correct solution.

A. 40%
B. 50%
C. 60%
D. 80%
E. 90%

KS15 · Answer

+1 for B. P(R or S) = P(R) + P(S) – P(R and S)
0.9 = 0.6 + 0.8 – P(R and S)
0.9 = 1.4 – P(R and S)
0.9 + P(R and S) = 1.4
P(R and S) = 0.5
Answer = (B)

pacifist85 · Answer

After drawing the venn diagram it makes more sense.

It is 60 + 80 - (Both) = 90 --> 140 - Both = 90 --> Both = 50. So,  ANS B

The reason we need the union is because the stem says "at least one rabbit AND at least one Songbird".

Bunuel · Answer

MAGOOSH OFFICIAL SOLUTION:

This is less about percents and more about probability, particularly the  probability OR-rule . Let R = the event that a young fox catches at least one rabbit, and let S = the event that a young fox catches at least one songbird. Using algebraic probability notation, we know P(R) = 0.8 and P(S) = 0.6. We know P((not R) and (not S)) = 0.1, and the complement of   would be  , so by the  complement rule , P(R or S) = 1 – 0.1 = 0.9. The question is asking for P(R and S). The OR rule tells us

P(R or S) = P(R) + P(S) – P(R and S)
0.9 = 0.6 + 0.8 – P(R and S)
0.9 = 1.4 – P(R and S)
0.9 + P(R and S) = 1.4
P(R and S) = 0.5

Answer = (B)

rohit8865 · Answer

10% of the young foxes never caught either a rabbit or a songbird,it means 90% foxes caught either a rabbit or a songbird.
then young foxes who successful in catching at least one rabbit and at least one songbird=young foxes caught a rabbit+young foxes caught a bird-young foxes caught both
=80+60-90=50%
Ans B

sdow · Answer

rabbit catch + songbird catch - both + neither
80+60-b+10=100
b=50
50% is the answer

A scientific research study examined a large number of young foxes

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A scientific research study examined a large number of young foxes

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