Answer :
Let's determine the probability of pulling out a white sock, not replacing it, and then pulling out another white sock from a drawer containing 2 red socks, 2 green socks, and 6 white socks.
Steps to find the probability:
1. Calculate the total number of socks:
There are 2 red socks, 2 green socks, and 6 white socks.
[tex]\[ \text{Total socks} = 2 + 2 + 6 = 10 \][/tex]
2. Probability of drawing the first white sock:
The probability of drawing a white sock from the 10 socks is:
[tex]\[ \frac{\text{Number of white socks}}{\text{Total number of socks}} = \frac{6}{10} = 0.6 \][/tex]
3. Update the total number of socks and white socks after drawing the first white sock:
After removing one white sock, there will be 5 white socks left and 9 socks in total.
4. Probability of drawing the second white sock:
The probability of drawing another white sock from the remaining 9 socks is:
[tex]\[ \frac{\text{Number of white socks left}}{\text{Total number of socks left}} = \frac{5}{9} \approx 0.5555555555555556 \][/tex]
5. Calculate the overall probability:
The combined probability of drawing two white socks in succession is:
[tex]\[ \text{Probability of first white sock} \times \text{Probability of second white sock} = 0.6 \times 0.5555555555555556 \approx 0.3333333333333333 \][/tex]
So, the correct choice among the given options is:
[tex]\[ \text{The probability that the first sock is white is } \left(\frac{6}{10}\right) \text{ and that the second sock is white is } \left(\frac{5}{9}\right), \text{ so the probability of choosing a pair of white socks is } \frac{30}{90} = \frac{1}{3}. \][/tex]
Steps to find the probability:
1. Calculate the total number of socks:
There are 2 red socks, 2 green socks, and 6 white socks.
[tex]\[ \text{Total socks} = 2 + 2 + 6 = 10 \][/tex]
2. Probability of drawing the first white sock:
The probability of drawing a white sock from the 10 socks is:
[tex]\[ \frac{\text{Number of white socks}}{\text{Total number of socks}} = \frac{6}{10} = 0.6 \][/tex]
3. Update the total number of socks and white socks after drawing the first white sock:
After removing one white sock, there will be 5 white socks left and 9 socks in total.
4. Probability of drawing the second white sock:
The probability of drawing another white sock from the remaining 9 socks is:
[tex]\[ \frac{\text{Number of white socks left}}{\text{Total number of socks left}} = \frac{5}{9} \approx 0.5555555555555556 \][/tex]
5. Calculate the overall probability:
The combined probability of drawing two white socks in succession is:
[tex]\[ \text{Probability of first white sock} \times \text{Probability of second white sock} = 0.6 \times 0.5555555555555556 \approx 0.3333333333333333 \][/tex]
So, the correct choice among the given options is:
[tex]\[ \text{The probability that the first sock is white is } \left(\frac{6}{10}\right) \text{ and that the second sock is white is } \left(\frac{5}{9}\right), \text{ so the probability of choosing a pair of white socks is } \frac{30}{90} = \frac{1}{3}. \][/tex]
