Without looking, George pulls socks from a drawer containing 2 white socks, 3 black socks, and 5 yellow socks. With each pulll, 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.
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?
To find the probability of drawing a yellow, black, and white sock in that order, we need to calculate the probability of each individual event and multiply them together.
Step 1: Determine the total number of socks in the drawer.
The total number of socks in the drawer is 2 white + 3 black + 5 yellow = 10 socks.
Step 2: Calculate the probability of drawing a yellow sock first.
The probability of drawing a yellow sock first is the number of yellow socks divided by the total number of socks: 5 yellow socks / 10 total socks = 1/2.
Step 3: Calculate the probability of drawing a black sock second.
Since we already removed a yellow sock from the drawer, there are now 4 yellow socks remaining. The total number of socks is reduced by 1, making it 10 - 1 = 9. The probability of drawing a black sock second is the number of black socks (3) divided by the total number of remaining socks (9): 3 black socks / 9 remaining socks = 1/3.
Step 4: Calculate the probability of drawing a white sock last.
Now, there are 2 white socks in a total of 8 remaining socks (10 - 2 - 1 = 7). So, the probability of drawing a white sock last is 2 white socks / 8 remaining socks = 1/4.
Step 5: Multiply the probabilities together.
To find the overall probability, we multiply the probabilities of each event together: (1/2) * (1/3) * (1/4) = 1/24.
Therefore, the probability of drawing a yellow, black, and white sock in that order is 1/24.
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
With each draw, there is one less sock total.
5/10 * 3/9 * 2/8 = ?