Question

Medal to the best answer!
A drawer contains 4 red socks, 3 white socks, and 3 blue socks. Without looking, you select a sock at random, replace it, and select a second sock at random. What is the probability that the first sock is blue and the second sock is red?

Answer 1

what's the probability of picking blue

Answer 2

3/10?

Answer 3

there are 3 blue socks

there are 4+3+3 = 10 socks total

so the probability of picking blue is 3/10

good catch

Answer 4

what's the probability of picking red

Answer 5

4/10

Answer 6

would the answer be 7/20?

Answer 7

so from here, you multiply the two probabilities because the two events are independent


P(Blue then red) = P(Blue AND Red)


P(Blue then red) = P(Blue)*P(Red)


P(Blue then red) = (3/10)*(4/10)


P(Blue then red) = (3*4)/(10*10)


P(Blue then red) = 12/100


P(Blue then red) = 3/25

Answer 8

Thanks @jim_thompson5910 !

Answer 9

yw

Answer 10

by multiplication rule there are 4X3X3 outcomes
P(R) = 4!/4X3X3=4X3X2/4X3X3=2/3
P(B) = 3!/4X3X3 = 3X2/4X3X3 = 1/6
use 3! because there 3X2X1 ways of selecting them
conditional probability
P(R|B) = P(R) because you used replacement
P(B and then R) = P(B)P(R|B) = 2/9

Answer 11

2/18