A drawer contains 8 red socks, 4 white socks, and 2 blue socks. Without looking, you draw out a sock,
return it, and draw out a second sock. What is the probability that the first sock is white and the second
sock is blue?
prob(white, then blue) , sock is returned after draw
= (4/14)(2/14)
= 2/49
if the first sock in not returned it would be
(4/14)(2/13) , just thought I would include that thought.
To find the probability of drawing a white sock and then a blue sock, we need to consider the total number of socks and the number of favorable outcomes.
Total number of socks = 8 (red socks) + 4 (white socks) + 2 (blue socks) = 14 socks
Since we are returning the first sock after drawing, the number of socks remains the same for the second draw.
Number of favorable outcomes:
For the first sock to be white, there are 4 white socks out of a total of 14 socks.
For the second sock to be blue, there are 2 blue socks out of a total of 14 socks.
To calculate the probability, we multiply the probabilities of each draw together:
P(white, blue) = (4/14) * (2/14) = 8/196 = 1/24
Therefore, the probability of drawing a white sock first and then a blue sock is 1/24.