We choose 2 different people - what is the probability that they all have the same color of the eyes
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So I have big problems with the problem above... I tried for like 5 hours to find the solution but I just don't know how to proceed. So, there are 45 people, and 5 eye colors. Dark Brown = 20; Blue = 10; Green = 8 ; Light-Brown = 4; Black = 3
I did a tree diagram and I multiplied the values for each, for example: P(D.Brown)= $frac{20}{45} cdot frac{19}{44} = 0.19$
After that, I don't know what to do..
edit: i forgot to mention that it says (draw without replacement)
probability statistics conditional-probability
asked Dec 10 '18 at 23:58
LarryLarry
104
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|
show 7 more comments
$begingroup$
So I have big problems with the problem above... I tried for like 5 hours to find the solution but I just don't know how to proceed. So, there are 45 people, and 5 eye colors. Dark Brown = 20; Blue = 10; Green = 8 ; Light-Brown = 4; Black = 3
I did a tree diagram and I multiplied the values for each, for example: P(D.Brown)= $frac{20}{45} cdot frac{19}{44} = 0.19$
After that, I don't know what to do..
edit: i forgot to mention that it says (draw without replacement)
probability statistics conditional-probability
asked Dec 10 '18 at 23:58
LarryLarry
104
$endgroup$
2
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Just go color by color and add. What's the probability that they both have dark brown eyes, say?
$endgroup$
– lulu
Dec 11 '18 at 0:01
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the probability that they both have dark brown eyes is 0,19 ; Blue = 0,5 ; Green = 0,03; Light-Brown = 0,06 and Black = 0,03. So you say that the answer is just the sum of these ?
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– Larry
Dec 11 '18 at 0:04
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The sum of it would be 0,81 , so 81% ?@lulu
$endgroup$
– Larry
Dec 11 '18 at 0:06
1
$begingroup$
Try a smaller problem you can do by listing all the cases. Suppose, say, $5$ people, $2$ with blue and $3$ with brown eyes. Count the pairs that match and divide by the total number of pairs. Then generalize.
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– Ethan Bolker
Dec 11 '18 at 0:12
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That seems too high. Blue, for instance, should be $frac {10}{45}times frac 9{44}=frac 1{22}$. Why would you think it was $.5$?
$endgroup$
– lulu
Dec 11 '18 at 0:14
|
show 7 more comments
$begingroup$
So I have big problems with the problem above... I tried for like 5 hours to find the solution but I just don't know how to proceed. So, there are 45 people, and 5 eye colors. Dark Brown = 20; Blue = 10; Green = 8 ; Light-Brown = 4; Black = 3
I did a tree diagram and I multiplied the values for each, for example: P(D.Brown)= $frac{20}{45} cdot frac{19}{44} = 0.19$
After that, I don't know what to do..
edit: i forgot to mention that it says (draw without replacement)
probability statistics conditional-probability
asked Dec 10 '18 at 23:58
LarryLarry
104
$endgroup$
So I have big problems with the problem above... I tried for like 5 hours to find the solution but I just don't know how to proceed. So, there are 45 people, and 5 eye colors. Dark Brown = 20; Blue = 10; Green = 8 ; Light-Brown = 4; Black = 3
I did a tree diagram and I multiplied the values for each, for example: P(D.Brown)= $frac{20}{45} cdot frac{19}{44} = 0.19$
After that, I don't know what to do..
edit: i forgot to mention that it says (draw without replacement)
probability statistics conditional-probability
probability statistics conditional-probability
asked Dec 10 '18 at 23:58
LarryLarry
104
asked Dec 10 '18 at 23:58
LarryLarry
104
edited Dec 11 '18 at 0:21
Larry
asked Dec 10 '18 at 23:58
LarryLarry
104
asked Dec 10 '18 at 23:58
LarryLarry
104
asked Dec 10 '18 at 23:58
LarryLarry
104
104
2
$begingroup$
Just go color by color and add. What's the probability that they both have dark brown eyes, say?
$endgroup$
– lulu
Dec 11 '18 at 0:01
$begingroup$
the probability that they both have dark brown eyes is 0,19 ; Blue = 0,5 ; Green = 0,03; Light-Brown = 0,06 and Black = 0,03. So you say that the answer is just the sum of these ?
$endgroup$
– Larry
Dec 11 '18 at 0:04
$begingroup$
The sum of it would be 0,81 , so 81% ?@lulu
$endgroup$
– Larry
Dec 11 '18 at 0:06
1
$begingroup$
Try a smaller problem you can do by listing all the cases. Suppose, say, $5$ people, $2$ with blue and $3$ with brown eyes. Count the pairs that match and divide by the total number of pairs. Then generalize.
$endgroup$
– Ethan Bolker
Dec 11 '18 at 0:12
$begingroup$
That seems too high. Blue, for instance, should be $frac {10}{45}times frac 9{44}=frac 1{22}$. Why would you think it was $.5$?
$endgroup$
– lulu
Dec 11 '18 at 0:14
|
show 7 more comments
2
$begingroup$
Just go color by color and add. What's the probability that they both have dark brown eyes, say?
$endgroup$
– lulu
Dec 11 '18 at 0:01
$begingroup$
the probability that they both have dark brown eyes is 0,19 ; Blue = 0,5 ; Green = 0,03; Light-Brown = 0,06 and Black = 0,03. So you say that the answer is just the sum of these ?
$endgroup$
– Larry
Dec 11 '18 at 0:04
$begingroup$
The sum of it would be 0,81 , so 81% ?@lulu
$endgroup$
– Larry
Dec 11 '18 at 0:06
1
$begingroup$
Try a smaller problem you can do by listing all the cases. Suppose, say, $5$ people, $2$ with blue and $3$ with brown eyes. Count the pairs that match and divide by the total number of pairs. Then generalize.
$endgroup$
– Ethan Bolker
Dec 11 '18 at 0:12
$begingroup$
That seems too high. Blue, for instance, should be $frac {10}{45}times frac 9{44}=frac 1{22}$. Why would you think it was $.5$?
$endgroup$
– lulu
Dec 11 '18 at 0:14
2
2
$begingroup$
Just go color by color and add. What's the probability that they both have dark brown eyes, say?
$endgroup$
– lulu
Dec 11 '18 at 0:01
$begingroup$
Just go color by color and add. What's the probability that they both have dark brown eyes, say?
$endgroup$
– lulu
Dec 11 '18 at 0:01
$begingroup$
the probability that they both have dark brown eyes is 0,19 ; Blue = 0,5 ; Green = 0,03; Light-Brown = 0,06 and Black = 0,03. So you say that the answer is just the sum of these ?
$endgroup$
– Larry
Dec 11 '18 at 0:04
$begingroup$
the probability that they both have dark brown eyes is 0,19 ; Blue = 0,5 ; Green = 0,03; Light-Brown = 0,06 and Black = 0,03. So you say that the answer is just the sum of these ?
$endgroup$
– Larry
Dec 11 '18 at 0:04
$begingroup$
The sum of it would be 0,81 , so 81% ?@lulu
$endgroup$
– Larry
Dec 11 '18 at 0:06
$begingroup$
The sum of it would be 0,81 , so 81% ?@lulu
$endgroup$
– Larry
Dec 11 '18 at 0:06
1
1
$begingroup$
Try a smaller problem you can do by listing all the cases. Suppose, say, $5$ people, $2$ with blue and $3$ with brown eyes. Count the pairs that match and divide by the total number of pairs. Then generalize.
$endgroup$
– Ethan Bolker
Dec 11 '18 at 0:12
$begingroup$
Try a smaller problem you can do by listing all the cases. Suppose, say, $5$ people, $2$ with blue and $3$ with brown eyes. Count the pairs that match and divide by the total number of pairs. Then generalize.
$endgroup$
– Ethan Bolker
Dec 11 '18 at 0:12
$begingroup$
That seems too high. Blue, for instance, should be $frac {10}{45}times frac 9{44}=frac 1{22}$. Why would you think it was $.5$?
$endgroup$
– lulu
Dec 11 '18 at 0:14
$begingroup$
That seems too high. Blue, for instance, should be $frac {10}{45}times frac 9{44}=frac 1{22}$. Why would you think it was $.5$?
$endgroup$
– lulu
Dec 11 '18 at 0:14
|
show 7 more comments
1 Answer
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oldest
votes
$begingroup$
You're right so far, but like you said you need to do more.
20/45*19/44= 19/99 (dark brown eyes)
10/45*9/44= 1/22 (blue eyes)
8/45*7/44= 14/495 (green eyes)
4/45*3/45= 1/165 (light brown eyes)
3/45*2/45= 1/330 (black eyes)
Now add all the answers up
19/99+1/22+14/495+1/165+1/330= 136/495
or in decimal form around 0.2747, or 27.5%
answered Dec 11 '18 at 0:17
THE CONFUSED PERSONTHE CONFUSED PERSON
183
$endgroup$
$begingroup$
Comments are not for extended discussion; this conversation has been moved to chat.
$endgroup$
– Aloizio Macedo♦
Dec 12 '18 at 14:01
add a comment |
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1 Answer
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1 Answer
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$begingroup$
You're right so far, but like you said you need to do more.
20/45*19/44= 19/99 (dark brown eyes)
10/45*9/44= 1/22 (blue eyes)
8/45*7/44= 14/495 (green eyes)
4/45*3/45= 1/165 (light brown eyes)
3/45*2/45= 1/330 (black eyes)
Now add all the answers up
19/99+1/22+14/495+1/165+1/330= 136/495
or in decimal form around 0.2747, or 27.5%
answered Dec 11 '18 at 0:17
THE CONFUSED PERSONTHE CONFUSED PERSON
183
$endgroup$
$begingroup$
Comments are not for extended discussion; this conversation has been moved to chat.
$endgroup$
– Aloizio Macedo♦
Dec 12 '18 at 14:01
add a comment |
$begingroup$
You're right so far, but like you said you need to do more.
20/45*19/44= 19/99 (dark brown eyes)
10/45*9/44= 1/22 (blue eyes)
8/45*7/44= 14/495 (green eyes)
4/45*3/45= 1/165 (light brown eyes)
3/45*2/45= 1/330 (black eyes)
Now add all the answers up
19/99+1/22+14/495+1/165+1/330= 136/495
or in decimal form around 0.2747, or 27.5%
answered Dec 11 '18 at 0:17
THE CONFUSED PERSONTHE CONFUSED PERSON
183
$endgroup$
$begingroup$
Comments are not for extended discussion; this conversation has been moved to chat.
$endgroup$
– Aloizio Macedo♦
Dec 12 '18 at 14:01
add a comment |
$begingroup$
You're right so far, but like you said you need to do more.
20/45*19/44= 19/99 (dark brown eyes)
10/45*9/44= 1/22 (blue eyes)
8/45*7/44= 14/495 (green eyes)
4/45*3/45= 1/165 (light brown eyes)
3/45*2/45= 1/330 (black eyes)
Now add all the answers up
19/99+1/22+14/495+1/165+1/330= 136/495
or in decimal form around 0.2747, or 27.5%
answered Dec 11 '18 at 0:17
THE CONFUSED PERSONTHE CONFUSED PERSON
183
$endgroup$
You're right so far, but like you said you need to do more.
20/45*19/44= 19/99 (dark brown eyes)
10/45*9/44= 1/22 (blue eyes)
8/45*7/44= 14/495 (green eyes)
4/45*3/45= 1/165 (light brown eyes)
3/45*2/45= 1/330 (black eyes)
Now add all the answers up
19/99+1/22+14/495+1/165+1/330= 136/495
or in decimal form around 0.2747, or 27.5%
answered Dec 11 '18 at 0:17
THE CONFUSED PERSONTHE CONFUSED PERSON
183
answered Dec 11 '18 at 0:17
THE CONFUSED PERSONTHE CONFUSED PERSON
183
answered Dec 11 '18 at 0:17
THE CONFUSED PERSONTHE CONFUSED PERSON
183
answered Dec 11 '18 at 0:17
THE CONFUSED PERSONTHE CONFUSED PERSON
183
183
$begingroup$
Comments are not for extended discussion; this conversation has been moved to chat.
$endgroup$
– Aloizio Macedo♦
Dec 12 '18 at 14:01
add a comment |
$begingroup$
Comments are not for extended discussion; this conversation has been moved to chat.
$endgroup$
– Aloizio Macedo♦
Dec 12 '18 at 14:01
$begingroup$
Comments are not for extended discussion; this conversation has been moved to chat.
$endgroup$
– Aloizio Macedo♦
Dec 12 '18 at 14:01
$begingroup$
Comments are not for extended discussion; this conversation has been moved to chat.
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– Aloizio Macedo♦
Dec 12 '18 at 14:01
add a comment |
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$begingroup$
Just go color by color and add. What's the probability that they both have dark brown eyes, say?
$endgroup$
– lulu
Dec 11 '18 at 0:01
$begingroup$
the probability that they both have dark brown eyes is 0,19 ; Blue = 0,5 ; Green = 0,03; Light-Brown = 0,06 and Black = 0,03. So you say that the answer is just the sum of these ?
$endgroup$
– Larry
Dec 11 '18 at 0:04
$begingroup$
The sum of it would be 0,81 , so 81% ?@lulu
$endgroup$
– Larry
Dec 11 '18 at 0:06
1
$begingroup$
Try a smaller problem you can do by listing all the cases. Suppose, say, $5$ people, $2$ with blue and $3$ with brown eyes. Count the pairs that match and divide by the total number of pairs. Then generalize.
$endgroup$
– Ethan Bolker
Dec 11 '18 at 0:12
$begingroup$
That seems too high. Blue, for instance, should be $frac {10}{45}times frac 9{44}=frac 1{22}$. Why would you think it was $.5$?
$endgroup$
– lulu
Dec 11 '18 at 0:14