A drawer contains two red socks three white socks and three 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
3/8
2/5
29/32
3/32
Pls help
There are a couple of ways to approach this problem, but one common method is to use the multiplication rule of probability. According to this rule, the probability of two independent events A and B both happening is the product of their individual probabilities: P(A and B) = P(A) x P(B).
In this case, let's define the events A and B as follows: A = "drawing a blue sock on the first draw" and B = "drawing a red sock on the second draw." We want to find the probability of A and B happening, or P(A and B).
The probability of drawing a blue sock on the first draw is 3/8, because there are 3 blue socks out of a total of 8 socks. Since we return the first sock before drawing the second one, the probabilities of the two draws are independent, meaning that the outcome of the first draw doesn't affect the probabilities of the second draw. Therefore, the probability of drawing a red sock on the second draw is also 2/8 or 1/4.
Now we can use the multiplication rule to find the probability of both events happening: P(A and B) = P(A) x P(B) = (3/8) x (1/4) = 3/32. Therefore, the answer is 3/32.