suppose a drawer contains 3 white socks, 6 brown socks, and 7 blue socks. We draw one sock from the drawer and it is equally likely that any one of the socks is drawn. Find the probabilities of the events in parts (a) - (e):
a. find the probability that the sock is brown.
b. find the probability that the sock is white or blue.
c. find the probability that the sock is black.
d. find the probability the sock is not white
e. we reach into the drawer without looking to pull out four socks. what is the probability that we will get at least 2 socks of the same color?
Part a
find the probability that the sock is brown
P=6/16 ------> simplify P=3/8
Part b
find the probability that the sock is white or blue
P=(3+7)/16 -----> P=10/16 ------> P=5/8
Part c
find the probability that the sock is black
P=0/16 ------> P=0
Part d
find the probability the sock is not white
P=13/16
Part e
we reach into the drawer without looking to pull out four socks. what is the probability that we will get at least 2 socks of the same color?
we have that
at least 2 socks of the same color means
2 socks of the same color
or
3 socks of the same color
or
4 socks of the same color
so
2C16 ------> find out the number of possible outcomes
2C16=16!/[(16-2)!*2!] -------> 2C16=(16*15*14!)/[14!*2!] ------> 2C16=120
we have
white/brown pairs ------> 3*6=18
white /blue pairs ------> 3*7=21
brown/blue pairs -----> 6*7=42
total mixed color pairs=18+21+42=81
number of same color pairs=120-81=39
probability of same pair color is P=39/120