Without looking, George pulls socks from a drawer containing 2 white socks, 3 black socks, and 5 yellow socks. With each pull, a sock is removed from the drawer and is not replaced. Find the probability of drawing a yellow, black, and white sock in that order?
do we had 5/10 +3/10+2/10?
no, you cant add them
notice you would have a probability equal to 1, which means the event you want will always happen.
prob(yellow, black, then white)
= (5/10)(3/9)(2/8)
= 1/24
notice that each time a sock is pulled there is one less to choose from, hence the decreasing denominators
To find the probability of drawing a yellow, black, and white sock in that order, we need to calculate the product of each individual probability.
First, let's find the probability of drawing a yellow sock on the first pull. There are 5 yellow socks out of a total of 10 socks in the drawer, so the probability of drawing a yellow sock is 5/10.
Next, after drawing a yellow sock, there are 9 socks left in the drawer. Now we need to find the probability of drawing a black sock on the second pull. There are 3 black socks out of the 9 remaining socks, so the probability of drawing a black sock is 3/9.
Finally, after drawing a black sock, there are 8 socks left in the drawer. Now we need to find the probability of drawing a white sock on the third pull. There are 2 white socks out of the 8 remaining socks, so the probability of drawing a white sock is 2/8.
To find the overall probability of drawing a yellow, black, and white sock in that order, we multiply the probabilities together:
(5/10) * (3/9) * (2/8) = 30/720 = 1/24.
Therefore, the probability of drawing a yellow, black, and white sock in that order is 1/24.