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
There are 8 socks, so
3/8 * 2/8
Well, let's see here. Drawing socks seems like a pretty exciting activity! So, we have 2 red socks, 3 white socks, and 3 blue socks in the drawer.
First, we need to find the probability of drawing a blue sock on the first try. There are a total of 8 socks in the drawer, and 3 of them are blue. So the probability of drawing a blue sock on the first try is 3/8.
Now, since we return the first sock before drawing the second one, the number of socks in the drawer remains the same. So, on the second try, there are still 8 socks, but now there's only 2 red socks left.
Therefore, the probability of drawing a red sock on the second try, given that the first sock was blue, is 2/8 or 1/4.
To find the probability of both events occurring, we simply multiply the probabilities: (3/8) * (1/4) = 3/32.
So, the answer is 3/32. Ah, sock it to me!
To find the probability that the first sock is blue and the second sock is red, we need to consider the total number of possible outcomes and the number of favorable outcomes.
The total number of possible outcomes is the product of the number of choices for each draw. Since there are 2 socks drawn with replacement, there are 3 possible choices for each draw. Therefore, the total number of possible outcomes is 3 * 3 = 9.
Now, let's determine the number of favorable outcomes. Since the first sock must be blue and the second sock must be red, we know that there are 3 choices for the first draw and 2 choices for the second draw. Therefore, the number of favorable outcomes is 3 * 2 = 6.
Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Favorable outcomes / Total outcomes = 6 / 9 = 2/3.
Therefore, the probability that the first sock is blue and the second sock is red is 2/3.
To find the probability of drawing a blue sock first and then a red sock, we need to determine the total number of possible outcomes and the number of favorable outcomes.
First, let's find the total number of possible outcomes. Since we return the sock after each draw, there are a total of (2 + 3 + 3) = 8 socks in the drawer, and we have two draws. So the total number of possible outcomes is 8 * 8 = 64.
Next, let's determine the number of favorable outcomes, which is the number of ways we can draw a blue sock first and then a red sock. There are 3 blue socks and 2 red socks in the drawer. So the number of favorable outcomes is 3 * 2 = 6.
Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes. Therefore, the probability is 6/64, which simplifies to 3/32.
Therefore, the probability that the first sock drawn is blue and the second sock is red is 3/32.