binomial help

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

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?

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 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?

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.

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