The Solution:
Given:
We are required to find the probability that the second sock is navy blue if the first one was a white sock.
Step 1:
The probability of the first sock being a white is:
[tex]P(first\text{ }W)=\frac{Number\text{ of white}}{Total\text{ number of socks}}=\frac{10}{14}=\frac{5}{7}[/tex]Step 2:
The probability of the second sock being a Navy blue is:
Note:
One sock has been taken out without replacement. So, the total number of socks is now 13.
[tex]P(second\text{ Navy Blue\rparen}=\frac{Number\text{ of navy blue socks}}{Current\text{ Total number of socks}}=\frac{4}{13}[/tex]Thus, the probability of the first being White and the second being Navy Blue is:
[tex]P(W\text{ NB})=P(W)\times P(NB)=\frac{5}{7}\times\frac{4}{13}=\frac{20}{91}=0.2198\approx0.22[/tex]Therefore, the correct answer is 20/91 or 0.22
