Let's solve this problem step by step:
1. Identify the total number of pairs of socks Deena has:
Deena has:
- 4 pairs of white socks,
- 3 pairs of black socks,
- 1 pair of red socks, and
- 2 pairs of navy socks.
To find the total number of pairs of socks, we need to sum these up:
[tex]\[
4 + 3 + 1 + 2 = 10
\][/tex]
So, Deena has a total of 10 pairs of socks.
2. Identify the number of pairs of white socks Deena has:
Deena has 4 pairs of white socks.
3. Calculate the probability of pulling out a pair of white socks:
The probability of an event is given by the ratio of the number of favorable outcomes to the total number of possible outcomes. In this case, the favorable outcomes are pulling out a pair of white socks, and the total possible outcomes are pulling out any pair of socks.
The probability [tex]\( P \)[/tex] of choosing a pair of white socks is:
[tex]\[
P = \frac{\text{Number of pairs of white socks}}{\text{Total number of pairs of socks}} = \frac{4}{10}
\][/tex]
4. Simplify the fraction (if necessary):
The fraction [tex]\(\frac{4}{10}\)[/tex] can be simplified by dividing the numerator and the denominator by their greatest common divisor, which is 2:
[tex]\[
\frac{4 \div 2}{10 \div 2} = \frac{2}{5}
\][/tex]
Hence, the probability that Deena will choose a pair of white socks is [tex]\(\frac{2}{5}\)[/tex].
5. Verify the answer by checking the options given:
The available options are:
[tex]\[
\frac{2}{3}, \frac{1}{4}, \frac{2}{5}, \frac{3}{5}
\][/tex]
Among these options, the correct probability [tex]\(\frac{2}{5}\)[/tex] matches one of the choices.
Therefore, the probability that Deena will choose a pair of white socks is [tex]\(\frac{2}{5}\)[/tex].
