binomial help

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CasualSoul
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#1
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#1
The probability it will rain on a certain day is 0.3. calculate the probabilitythat in a particular week in April it will rain on exactly three consecutive. Days. I keep getting 0.2268. first time I used combinations and then I did it another way using factorials. Apparantly the answer is 0.0324 I've spent over 2 hours on this reading up notes etcbut I really don't understand how to get the answer any help would be great cos I'm pretty stuck :C
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Notnek
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#2
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(Original post by CasualSoul)
The probability it will rain on a certain day is 0.3. calculate the probabilitythat in a particular week in April it will rain on exactly three consecutive. Days. I keep getting 0.2268. first time I used combinations and then I did it another way using factorials. Apparantly the answer is 0.0324 I've spent over 2 hours on this reading up notes etcbut I really don't understand how to get the answer any help would be great cos I'm pretty stuck :C
Firstly, how many ways can 3 consecutive days of rain occur in a certain week? Here's an example of one way : NRRRNNN (R means rain and N means no rain).

Then for each of these, the probability of it occuring will be 0.3^3 multiplied by _____. Can you fill in the blank?


Side note: The thing that makes this different to a regular binomial probability question is the word consecutive.

If the question asked, "calculate... it will rain on three days" then you could just plug numbers into the binomial probability formula. Students often use the binomial formula without knowing why, which can cause problems when questions like this come up.

Using 5C3 for this question would not give you the number of ways that you can arrange 3 consecutive days into a given week.
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BabyMaths
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I can get that answer: 0.0324135 or 64827/2000000 but I think that as it's worded here the question is a little more interesting. It does not exclude cases like NRRRNRR does it?
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Notnek
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(Original post by BabyMaths)
I can get that answer: 0.0324135 or 64827/2000000 but I think that as it's worded here the question is a little more interesting. It does not exclude cases like NRRRNRR does it?
The question is not worded perfectly but I think the use of the word exactly excludes cases like the one you mentioned.

If it said "Calculate the probability that in a particular week in April it will rain on three consecutive days" then NRRRNRR may be allowed.
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CasualSoul
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#5
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I
(Original post by notnek)
Firstly, how many ways can 3 consecutive days of rain occur in a certain week? Here's an example of one way : NRRRNNN (R means rain and N means no rain).

Then for each of these, the probability of it occuring will be 0.3^3 multiplied by _____. Can you fill in the blank?


Side note: The thing that makes this different to a regular binomial probability question is the word consecutive.

If the question asked, "calculate... it will rain on three days" then you could just plug numbers into the binomial probability formula. Students often use the binomial formula without knowing why, which can cause problems when questions like this come up.

Using 5C3 for this question would not give you the number of ways that you can arrange 3 consecutive days into a given week.
I firstly said p (RRRNNNN) IS 0.00648. But we have 7 different ways of ordering so I calculated 7 factorial then i said RRR is 3 factorial . and NNNN is 4 factorial. If something can happen in m different ways and after that has happen something else can be chosen in n different ways you multiply m and n. So I multiplied 3 factoria/ and 4 factorial. I then did 7 factorial divided by ( 3 factorial times 4 factorial to account for this) then I multiplied my answer by 0.00648 giving 0.2268. I understand why normal binomial isn't used Like you said but I'm just a bit. confused as to what to do
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CasualSoul
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#6
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(Original post by BabyMaths)
I can get that answer: 0.0324135 or 64827/2000000 but I think that as it's worded here the question is a little more interesting. It does not exclude cases like NRRRNRR does it?
Yeah it excludes cases like that as it says exaxtly 3
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Notnek
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(Original post by CasualSoul)
I

I firstly said p (RRRNNNN) IS 0.00648. But we have 7 different ways of ordering so I calculated 7 factorial then i said RRR is 3 factorial . and NNNN is 4 factorial. If something can happen in m different ways and after that has happen something else can be chosen in n different ways you multiply m and n. So I multiplied 3 factoria/ and 4 factorial. I then did 7 factorial divided by ( 3 factorial times 4 factorial to account for this) then I multiplied my answer by 0.00648 giving 0.2268. I understand why normal binomial isn't used Like you said but I'm just a bit. confused as to what to do
0.00648 is correct for P(RRRNNNN).

7 factorial divided by ( 3 factorial times 4 factorial) is the same as 7C3 (7 choose 3). This is the number of ways you can arrange 3 rain days into a given week but you have forgotten about the "consecutive" restriction.

Ignore everything you've learnt about binomial probability and factorials and think about this : How many ways can you arrange 3 consecutive rain days into a given week? Try listing them and you should find that the question is simpler than you're making it.
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CasualSoul
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#8
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(Original post by notnek)
0.00648 is correct for P(RRRNNNN).

7 factorial divided by ( 3 factorial times 4 factorial) is the same as 7C3 (7 choose 3). This is the number of ways you can arrange 3 rain days into a given week but you have forgotten about the "consecutive" restriction.

Ignore everything you've learnt about binomial probability and factorials and think about this : How many ways can you arrange 3 consecutive rain days into a given week? Try listing them and you should find that the question is simpler than you're making it.
I got 720 for the above. But I still don't know what to do. I'm going to have to see one of the teachers
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Notnek
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#9
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(Original post by CasualSoul)
I got 720 for the above. But I still don't know what to do. I'm going to have to see one of the teachers
You're still overcomplicating it. Imagine you're a Y8 student who hasn't learnt about factorials. How many ways can you arrange 3 letter R's (that must stay together) into 7 spaces? I'll give you three ways:

RRRNNNN, NRRRNNN, NNRRRNN

How many more ways are there? Just list them.
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M_YB
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#10
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#10
So is it 0.03241
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