Question 974002
{{{4+6+8=18}}} , so there are {{{18}}} socks in the drawer.
Since {{{4/18=2/9}}} of them are red,
and any sock is as likely to be picked as any other,
the probability that the first sock picked is red is {{{2/9}}} .
Before the second pick, there are {{{18}}} socks in the drawer.
Since {{{8/18=4/9}}} of them are blue,
and any sock is as likely to be picked as any other,
the probability that the second sock picked is blue is {{{4/9}}} .
Whatever happened during the fist pick does not matter .
The two events are independent (and your teacher says to multiply the two probabilities when events are independent).
There is a good logical reason for multiplying:
For a first pick, {{{2/9}}} of the times you would get a red sock,
and {{{4/9}}} of those times, your second pick would be blue.
So {{{4/9}}} of {{{2/9}}} = {{{(4/9)(2/9)=8/81}}} of the times
you would pick a red sock on your first try and a blue sock on your second pick.
The probability of that chain of events is {{{highlight(8/81)}}} .