A drawer contains 2 red socks, 3 white socks, and 3 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 blue and the second sock is red?
Since you are returning the sock, the 2nd event is independent of the first.
so prob(your event) = (3/8)(2/8) = ...
To find the probability of drawing a blue sock followed by a red sock, we need to determine the total number of possible outcomes and the number of favorable outcomes.
First, let's calculate the total number of possible outcomes. Since you draw one sock, return it, and then draw another, there are a total of 9 socks in the drawer for the first draw, and 9 socks for the second draw. So the total number of possible outcomes is 9 * 9 = 81.
Next, let's determine the number of favorable outcomes, which is the scenario where the first sock is blue and the second sock is red.
The number of blue socks is 3, and the number of red socks is 2. So the number of favorable outcomes is 3 * 2 = 6.
Now, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes.
Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes
= 6 / 81
= 2 / 27
Therefore, the probability of selecting a blue sock followed by a red sock is 2/27.