Probability of drawing same ball until draw 4 or 'greater'?
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I'm working on the series of two different questions.
I got the first problem without difficulty but got stuck with second problem.
Here is the first problem I'm writing for context.
You have a bag containing $2$ red balls, $4$ green balls, and $5$ purple balls. You draw one ball from the bag: it's green. Call this draw $0$. Keep this ball and continue drawing (without replacement) until you get another green ball. Call these draws $1, 2...k$. What is the probability that you don't draw another green ball until draw $3$?
I got the answer by $largefrac{7}{10} cdot frac{6}{9} cdot frac{3}{8} = 0.175$, which was right.
However, next problem is somewhat tricky by its wording.
Resetting the original scenario such that draw $0$ yields a green ball, what is the probability that you don't draw another green ball until draw $4$ or greater?
I can't understand how can I get the answer for '$4$ or greater'. I just assumed it similar to first one and ended up with the answer $0.125 (largefrac{7}{10} cdot frac{6}{9} cdot frac{5}{8} cdot frac{3}{7})$ but it wasn't accurate.
What should I do for '$4$ or greater'?
probability statistics
edited Dec 8 '18 at 22:11
Gaby Alfonso
839316
asked Dec 8 '18 at 21:53
Daniel KimDaniel Kim
111
$endgroup$
add a comment |
$begingroup$
I'm working on the series of two different questions.
I got the first problem without difficulty but got stuck with second problem.
Here is the first problem I'm writing for context.
You have a bag containing $2$ red balls, $4$ green balls, and $5$ purple balls. You draw one ball from the bag: it's green. Call this draw $0$. Keep this ball and continue drawing (without replacement) until you get another green ball. Call these draws $1, 2...k$. What is the probability that you don't draw another green ball until draw $3$?
I got the answer by $largefrac{7}{10} cdot frac{6}{9} cdot frac{3}{8} = 0.175$, which was right.
However, next problem is somewhat tricky by its wording.
Resetting the original scenario such that draw $0$ yields a green ball, what is the probability that you don't draw another green ball until draw $4$ or greater?
I can't understand how can I get the answer for '$4$ or greater'. I just assumed it similar to first one and ended up with the answer $0.125 (largefrac{7}{10} cdot frac{6}{9} cdot frac{5}{8} cdot frac{3}{7})$ but it wasn't accurate.
What should I do for '$4$ or greater'?
probability statistics
edited Dec 8 '18 at 22:11
Gaby Alfonso
839316
asked Dec 8 '18 at 21:53
Daniel KimDaniel Kim
111
$endgroup$
1
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Hint: Getting the first green ball at draw $4$ or later is the same as saying "none of the draws up until draw $4$ are green."
$endgroup$
– platty
Dec 8 '18 at 22:00
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Hi platty, what's the difference between what you just said 'none of the draws up until draw 4 are green' and my last answer (7/10 * 6/9 * 5/8 * 3/7)?
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– Daniel Kim
Dec 8 '18 at 22:08
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never mind, I got it now! thank you for hint!
$endgroup$
– Daniel Kim
Dec 8 '18 at 22:10
$begingroup$
Notice that the event that you don't draw another green ball until draw $4$ or later is the complement of the event that you draw another green ball during the first three draws.
$endgroup$
– N. F. Taussig
Dec 8 '18 at 22:39
$begingroup$
Leave out the $frac{3}{7}$ factor in your answer.
$endgroup$
– herb steinberg
Dec 8 '18 at 22:52
add a comment |
$begingroup$
I'm working on the series of two different questions.
I got the first problem without difficulty but got stuck with second problem.
Here is the first problem I'm writing for context.
You have a bag containing $2$ red balls, $4$ green balls, and $5$ purple balls. You draw one ball from the bag: it's green. Call this draw $0$. Keep this ball and continue drawing (without replacement) until you get another green ball. Call these draws $1, 2...k$. What is the probability that you don't draw another green ball until draw $3$?
I got the answer by $largefrac{7}{10} cdot frac{6}{9} cdot frac{3}{8} = 0.175$, which was right.
However, next problem is somewhat tricky by its wording.
Resetting the original scenario such that draw $0$ yields a green ball, what is the probability that you don't draw another green ball until draw $4$ or greater?
I can't understand how can I get the answer for '$4$ or greater'. I just assumed it similar to first one and ended up with the answer $0.125 (largefrac{7}{10} cdot frac{6}{9} cdot frac{5}{8} cdot frac{3}{7})$ but it wasn't accurate.
What should I do for '$4$ or greater'?
probability statistics
edited Dec 8 '18 at 22:11
Gaby Alfonso
839316
asked Dec 8 '18 at 21:53
Daniel KimDaniel Kim
111
$endgroup$
I'm working on the series of two different questions.
I got the first problem without difficulty but got stuck with second problem.
Here is the first problem I'm writing for context.
You have a bag containing $2$ red balls, $4$ green balls, and $5$ purple balls. You draw one ball from the bag: it's green. Call this draw $0$. Keep this ball and continue drawing (without replacement) until you get another green ball. Call these draws $1, 2...k$. What is the probability that you don't draw another green ball until draw $3$?
I got the answer by $largefrac{7}{10} cdot frac{6}{9} cdot frac{3}{8} = 0.175$, which was right.
However, next problem is somewhat tricky by its wording.
Resetting the original scenario such that draw $0$ yields a green ball, what is the probability that you don't draw another green ball until draw $4$ or greater?
I can't understand how can I get the answer for '$4$ or greater'. I just assumed it similar to first one and ended up with the answer $0.125 (largefrac{7}{10} cdot frac{6}{9} cdot frac{5}{8} cdot frac{3}{7})$ but it wasn't accurate.
What should I do for '$4$ or greater'?
probability statistics
probability statistics
edited Dec 8 '18 at 22:11
Gaby Alfonso
839316
asked Dec 8 '18 at 21:53
Daniel KimDaniel Kim
111
edited Dec 8 '18 at 22:11
Gaby Alfonso
839316
asked Dec 8 '18 at 21:53
Daniel KimDaniel Kim
111
edited Dec 8 '18 at 22:11
Gaby Alfonso
839316
edited Dec 8 '18 at 22:11
Gaby Alfonso
839316
edited Dec 8 '18 at 22:11
Gaby Alfonso
839316
839316
asked Dec 8 '18 at 21:53
Daniel KimDaniel Kim
111
asked Dec 8 '18 at 21:53
Daniel KimDaniel Kim
111
asked Dec 8 '18 at 21:53
Daniel KimDaniel Kim
111
111
1
$begingroup$
Hint: Getting the first green ball at draw $4$ or later is the same as saying "none of the draws up until draw $4$ are green."
$endgroup$
– platty
Dec 8 '18 at 22:00
$begingroup$
Hi platty, what's the difference between what you just said 'none of the draws up until draw 4 are green' and my last answer (7/10 * 6/9 * 5/8 * 3/7)?
$endgroup$
– Daniel Kim
Dec 8 '18 at 22:08
$begingroup$
never mind, I got it now! thank you for hint!
$endgroup$
– Daniel Kim
Dec 8 '18 at 22:10
$begingroup$
Notice that the event that you don't draw another green ball until draw $4$ or later is the complement of the event that you draw another green ball during the first three draws.
$endgroup$
– N. F. Taussig
Dec 8 '18 at 22:39
$begingroup$
Leave out the $frac{3}{7}$ factor in your answer.
$endgroup$
– herb steinberg
Dec 8 '18 at 22:52
add a comment |
1
$begingroup$
Hint: Getting the first green ball at draw $4$ or later is the same as saying "none of the draws up until draw $4$ are green."
$endgroup$
– platty
Dec 8 '18 at 22:00
$begingroup$
Hi platty, what's the difference between what you just said 'none of the draws up until draw 4 are green' and my last answer (7/10 * 6/9 * 5/8 * 3/7)?
$endgroup$
– Daniel Kim
Dec 8 '18 at 22:08
$begingroup$
never mind, I got it now! thank you for hint!
$endgroup$
– Daniel Kim
Dec 8 '18 at 22:10
$begingroup$
Notice that the event that you don't draw another green ball until draw $4$ or later is the complement of the event that you draw another green ball during the first three draws.
$endgroup$
– N. F. Taussig
Dec 8 '18 at 22:39
$begingroup$
Leave out the $frac{3}{7}$ factor in your answer.
$endgroup$
– herb steinberg
Dec 8 '18 at 22:52
1
1
$begingroup$
Hint: Getting the first green ball at draw $4$ or later is the same as saying "none of the draws up until draw $4$ are green."
$endgroup$
– platty
Dec 8 '18 at 22:00
$begingroup$
Hint: Getting the first green ball at draw $4$ or later is the same as saying "none of the draws up until draw $4$ are green."
$endgroup$
– platty
Dec 8 '18 at 22:00
$begingroup$
Hi platty, what's the difference between what you just said 'none of the draws up until draw 4 are green' and my last answer (7/10 * 6/9 * 5/8 * 3/7)?
$endgroup$
– Daniel Kim
Dec 8 '18 at 22:08
$begingroup$
Hi platty, what's the difference between what you just said 'none of the draws up until draw 4 are green' and my last answer (7/10 * 6/9 * 5/8 * 3/7)?
$endgroup$
– Daniel Kim
Dec 8 '18 at 22:08
$begingroup$
never mind, I got it now! thank you for hint!
$endgroup$
– Daniel Kim
Dec 8 '18 at 22:10
$begingroup$
never mind, I got it now! thank you for hint!
$endgroup$
– Daniel Kim
Dec 8 '18 at 22:10
$begingroup$
Notice that the event that you don't draw another green ball until draw $4$ or later is the complement of the event that you draw another green ball during the first three draws.
$endgroup$
– N. F. Taussig
Dec 8 '18 at 22:39
$begingroup$
Notice that the event that you don't draw another green ball until draw $4$ or later is the complement of the event that you draw another green ball during the first three draws.
$endgroup$
– N. F. Taussig
Dec 8 '18 at 22:39
$begingroup$
Leave out the $frac{3}{7}$ factor in your answer.
$endgroup$
– herb steinberg
Dec 8 '18 at 22:52
$begingroup$
Leave out the $frac{3}{7}$ factor in your answer.
$endgroup$
– herb steinberg
Dec 8 '18 at 22:52
add a comment |
0
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1
$begingroup$
Hint: Getting the first green ball at draw $4$ or later is the same as saying "none of the draws up until draw $4$ are green."
$endgroup$
– platty
Dec 8 '18 at 22:00
$begingroup$
Hi platty, what's the difference between what you just said 'none of the draws up until draw 4 are green' and my last answer (7/10 * 6/9 * 5/8 * 3/7)?
$endgroup$
– Daniel Kim
Dec 8 '18 at 22:08
$begingroup$
never mind, I got it now! thank you for hint!
$endgroup$
– Daniel Kim
Dec 8 '18 at 22:10
$begingroup$
Notice that the event that you don't draw another green ball until draw $4$ or later is the complement of the event that you draw another green ball during the first three draws.
$endgroup$
– N. F. Taussig
Dec 8 '18 at 22:39
$begingroup$
Leave out the $frac{3}{7}$ factor in your answer.
$endgroup$
– herb steinberg
Dec 8 '18 at 22:52