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kath_the_great4
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similar question was posted earlier. See the link
https://www.beatthegmat.com/arrows-proba ... 18789.html
prob prob
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Source: Beat The GMAT — Problem Solving |
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manulath
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This question is slightly diff as it asks prob for ATLEAST 2 times
find probalility of no hit + probability of exactly 1 hit
then subtract the sum from 1
probability of hit = 1/4
probability of miss = 3/4
5 try - no hits = (3/4)^5
1 hit= 5C1*(1/4)*(3/4)^4 = 5*3^4/4^5
At least two hits = 1 - (3/4)^5 - 5*3^4/4^5
= (4^5 - 3^5 - 5*3^4) / 4^5
= 47/128
find probalility of no hit + probability of exactly 1 hit
then subtract the sum from 1
probability of hit = 1/4
probability of miss = 3/4
5 try - no hits = (3/4)^5
1 hit= 5C1*(1/4)*(3/4)^4 = 5*3^4/4^5
At least two hits = 1 - (3/4)^5 - 5*3^4/4^5
= (4^5 - 3^5 - 5*3^4) / 4^5
= 47/128
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manulath
- Senior | Next Rank: 100 Posts
- Posts: 35
- Joined: Tue Sep 09, 2008 10:12 pm
- Location: Lko
- Thanked: 3 times
This question is slightly diff as it asks prob for ATLEAST 2 times
find probalility of no hit + probability of exactly 1 hit
then subtract the sum from 1
probability of hit = 1/4
probability of miss = 3/4
5 try - no hits = (3/4)^5
1 hit= 5C1*(1/4)*(3/4)^4 = 5*3^4/4^5
At least two hits = 1 - (3/4)^5 - 5*3^4/4^5
= (4^5 - 3^5 - 5*3^4) / 4^5
= 47/128
find probalility of no hit + probability of exactly 1 hit
then subtract the sum from 1
probability of hit = 1/4
probability of miss = 3/4
5 try - no hits = (3/4)^5
1 hit= 5C1*(1/4)*(3/4)^4 = 5*3^4/4^5
At least two hits = 1 - (3/4)^5 - 5*3^4/4^5
= (4^5 - 3^5 - 5*3^4) / 4^5
= 47/128
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manulath
- Senior | Next Rank: 100 Posts
- Posts: 35
- Joined: Tue Sep 09, 2008 10:12 pm
- Location: Lko
- Thanked: 3 times
well just try and add the probabilities for 2 hits, 3 hits, 4 hits and 5 hits
i still had 47/128
(4^5 - 3^5 - 5*3^4) / 4^5
-3^5 - 5*3^4 can be simplified to
-3^4(3+5) = 8*3^4
hence numerator becomes 4^5 - 8*3^4
4^5 = 2^10 = 2^3*2^5 = 8*2^5 = 8*128
3^4 = 81
8*128 - 8*81 = 8*47
ans= 8*47 / 4^5 = 8*47/ 8*128 = 47/128
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= 47/128
i still had 47/128
(4^5 - 3^5 - 5*3^4) / 4^5
-3^5 - 5*3^4 can be simplified to
-3^4(3+5) = 8*3^4
hence numerator becomes 4^5 - 8*3^4
4^5 = 2^10 = 2^3*2^5 = 8*2^5 = 8*128
3^4 = 81
8*128 - 8*81 = 8*47
ans= 8*47 / 4^5 = 8*47/ 8*128 = 47/128
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= 47/128
