A drawer contains 2 red socks, 3 white socks, 3 blue socks. Without looking , you draw out a sock, then return it, and draw a second sock. What is the probability that the first sock is blue and the second is red? 3/8, 2/5, 29/32, 3/32 I chose 3/8 is that correct
I really need some help please anyone
To solve this problem, we need to calculate the probability of drawing a blue sock on the first draw and a red sock on the second draw.
Let's break it down step by step:
Step 1: Calculate the probability of drawing a blue sock on the first draw.
The total number of socks in the drawer is 2 red + 3 white + 3 blue = 8 socks.
The number of blue socks is 3.
Therefore, the probability of drawing a blue sock on the first draw is 3/8.
Step 2: Calculate the probability of drawing a red sock on the second draw.
After returning the first sock, we are left with the same number of socks: 2 red + 3 white + 3 blue = 8 socks.
The number of red socks is 2.
Therefore, the probability of drawing a red sock on the second draw is 2/8 or 1/4.
Step 3: Multiply the probabilities.
To find the combined probability, we multiply the individual probabilities from step 1 and step 2.
Probability of the first sock being blue and the second sock being red = (3/8) * (1/4) = 3/32.
Based on the calculations, the correct answer would be 3/32, not 3/8.