1. ## Probability (for socks)

Suppose there are 4 blue, 4 white and 4 gray socks in a dresser. For each of the following, determine an arithmetic expression (for example 1/2 * 1/2)

a.) Pulling at sock at random, whats the probability that that sock is white?

b.) Pulling a sock at random, whats the probability its not white?

c.) Pulling a sock at random, whats the probability that it is gray or white?

d.) Pulling a sock at random, whats the probability that its white and gray?

e.) Pulling out 2 socks (at random) in a row, whats the probability both are gray?

f.) Pulling out 2 socks (at random) in a row, whats the probability that 1 is blue and then the other is gray?

g.) Pulling out 2 socks (at random) in a row, whats the probability that itdoes not have a matching pair?

h.) Pulling out 2 socks (at random) in a row, whats the probability that you do have a matching pair?

i.) Determine the number of socks you have to remove at random to guarantee that you would have a pair.

What I think:

a.) 1/3
b.) 1 - 1/3 = 2/3
c.) 2/3
d.) 0 since you're only picking out 1? Maybe hte professor meant pulling 2 socks at random - if thats the case, what would it be
e.) (1/3)(1/3) = 1/9
f.) (1/3)(1/3) = 1/9
g.) Not sure
h.) not sure
i.) not sure

2. i think e and f is wrong should be. This is my answer :

e. 1/3 x 3/11 = 3/33 = 1/11
f. 1/3 x 4/11 = 4/33
g. 1/3 x 8/11 = 8/33
h. 1 - 8/33 = 25/33
i. My answer is 4 socks
No of pigeonhole = 3
ceiling function( x/3 ) = 2
Therefore x = 4