Question

14 socks in a drawer . Four of them are navy blue and 10 white What’s the probability that the second sock is navy blue if the first one was white

Answer 1

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:

`P(first\text{ }W)=\frac{Number\text{ of white}}{Total\text{ number of socks}}=(10)/(14)=(5)/(7)`

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.

`P(second\text{ Navy Blue\rparen}=\frac{Number\text{ of navy blue socks}}{Current\text{ Total number of socks}}=(4)/(13)`

Thus, the probability of the first being White and the second being Navy Blue is:

`P(W\text{ NB})=P(W)* P(NB)=(5)/(7)*(4)/(13)=(20)/(91)=0.2198\approx0.22`

Therefore, the correct answer is 20/91 or 0.22