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

##### Junior Member
We must assume here that we are taking the socks out blindly.
If you take out three socks, you might get 1 yellow 1 red and 1 orange. If you take out 4 socks you must get at least one pair of identical socks. Think about it.
A follow up question: How many socks do you have to take out to have two yellow socks?
7+6+2 = 15

##### Junior Member
t=0 ... 1 mosquito
t=2 … original 1 mosquito + 2 mosquitoes = 3 mosquitoes
t=3 … 3 mosquitoes + 1x2 mosquitoes = 5 mosquitoes (the new two aren't ready to "reproduce" yet)
t=4 … 5 mosquitoes + 3x2 mosquitoes = 11 mosquitoes (the new two aren't read to "reproduce" yet)
t=5 … 11 + 5x2 =21
t=6 … 21 + 5x2 =31
t=7 ....31+ 5x2 =41
t=8 .... 41 + 5x2 =51

right? I'm not totally confident about my answer because I still miss the concept of how you're multiplying at each step and what to include or not include of mosquitoes at each step still confused.

##### Junior Member
So at t=8 ; I have 30 mosquito?

#### Harry_the_cat

##### Senior Member
Did you continue the process?

##### Junior Member
So please how could I be verified of my answer? it would be just a honor please if you can help me!

#### Harry_the_cat

##### Senior Member
So please how could I be verified of my answer? it would be just a honor please if you can help me!
t=4 … M M M M M M M M M M M
What's the next row? It's your job to do the work, not mine!

##### Junior Member
what's confused me right now, if they asked what's mosquitoes at t=8 , will I include what's generated at t=8? which means the result should be the number of mosquitoes after t=8?

##### Junior Member
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