suppos a drawer contains 6 black socks, 4 brown socks, and 2 green socks. suppose one sock gets pulled out of the drawer and that is equally likely that any one of the socks is drawn. what is the probability that the sock is either balck or green.
the sock is not black.
Are these two different questions?
anyway there are 12 socks
probability of black = 6/12
probability of green = 2/12
probability black or green = 8/12 =2/3
probability that the sock is not black = 1 - probability of black = 1 -6/12 = 6/12 = 0.5
To solve this problem, let's first calculate the total number of socks in the drawer:
Total number of socks = 6 black + 4 brown + 2 green = 12 socks
Now, let's calculate the probability of drawing a black sock:
Probability of drawing a black sock = Number of black socks / Total number of socks
= 6 black socks / 12 socks
= 1/2
Next, let's calculate the probability of drawing a green sock:
Probability of drawing a green sock = Number of green socks / Total number of socks
= 2 green socks / 12 socks
= 1/6
Since we know the sock is not black, we need to calculate the probability of drawing a green sock given that it is not black:
Probability of drawing a green sock, given not black = Probability of drawing a green sock / Probability of not drawing a black sock
Probability of not drawing a black sock = 1 - Probability of drawing a black sock
= 1 - 1/2
= 1/2
So, the probability of drawing a green sock, given not black = (1/6) / (1/2)
= 1/6 * 2/1
= 1/3
Now, to find the probability of drawing either a black or a green sock, we can add the probabilities:
Probability of drawing either black or green = Probability of drawing a black sock + Probability of drawing a green sock
Probability of drawing either black or green = 1/2 + 1/3
= (3/6) + (2/6)
= 5/6
Therefore, the probability of drawing a sock that is either black or green, given that it is not black, is 5/6.
To find the probability that the sock is either black or green, given that the sock is not black, we need to first determine the total number of non-black socks in the drawer.
Given that there are 6 black socks, 4 brown socks, and 2 green socks, the total number of non-black socks would be 4 brown socks and 2 green socks, which equals 6 non-black socks in total.
Since the sock is not black, it can only be one of the 6 non-black socks. Therefore, the probability of drawing a non-black sock is 6/12 or 1/2.
So, the probability that the sock is either black or green, given that it is not black, is the same as the probability of it being green, which is 2/12 or 1/6.
Therefore, the probability that the sock is either black or green, given that it is not black, is 1/6.