Problems in math of probabilities: 5 yellow socks, 6 red socks, 7 orange socks; magic mosquitoes

[Dr.Peterson]

here's other question to prove that I understand, lets assume now that at every two seconds they will be generated one mosquitoes, how many mosquitoes will be at 6.5(at 6) ?
here's my answer and re-correct me if I'm wrong please! :
t=0 ... 1 mosquito
t=1 .... 1+1
t=2 ..... 2+1*1
t=3 ..... 3+2*1
t=4 .... 5+3*1
t=5 .... 8+5*1
t=6 .... 13+(8*1) = 21

so at t=6 there're 21 mosquitoes ... right?!

That is not the answer to the problem as you stated it. It would be correct if every second, each mosquito more than one second old produced one more.

Do you see the two differences?

But it's not telling me that; it tells me that once created mosquito at t=0 then at every more one second the current mosquitoes will generate one more mosquito

My comment was about the wording you used in stating this problem; it's not that your thinking is wrong, but that you misstated the problem. And you are stating it yet another way this time. Do you see how each of the statements quoted above is different? Wording is extremely important. That's one reason we have trouble with inaccurately translated problems.

As I said, if the problem you were solving was what I stated, then you got it right.

 

[Ryan$]

Then let me tell you exactly how the problem stated.
it's literally stated as this:
there's a mosquito created at t=0, after 2 seconds, it's starting to create mosquito over every second ! , what's the number of mosquito at t=8.5(after 8 seconds?) ?!
my answer is 34, am I right?! thanks alot

 

[Ryan$]

maybe it's 64? idk

 

[Dr.Peterson]

As I said, this kind of problem is sensitive to variations in wording; it is also hard to state clearly. I don't consider this version any clearer! It is not stated that every mosquito, after being "created" from another mosquito, like the first only starts creating more after 2 seconds.

I take it that way despite the ambiguity; that makes this the usual Fibonacci sequence. That is what you showed in the post I was answering, except that it is delayed by one second from what you showed (making the total 34 after 8 seconds).

 

[Otis]

… let me tell you exactly how the problem stated.
it's literally stated as this:
there's a mosquito created at t=0, after 2 seconds, it's starting to create mosquito over every second …

I don't believe that.

 

[Denis]

There is a mosquito created in time 0 ,
after two seconds he starts to generate at every second "two mosquito"

0....1....2....3....4....5....6....7....8 (seconds)
1................2.....2....2....2....2....2 = 13 (father + 12 sons!)

Is that the way you see it, or does Dad start to produce 2 at second#2, so ending with 14 sons?

 

[Steven G]

7+6+2 = 15

Correct.