To solve the problem, we need to determine the probability that Malachi will not pick a white sock from the laundry hamper.
First, let's find out how many socks are white. We know there are 100 socks in total, and the numbers of black, blue, and red socks are given as follows:
- Black socks: 24
- Blue socks: 19
- Red socks: 12
To find the number of white socks, we subtract the numbers of black, blue, and red socks from the total number of socks:
[tex]\[
\text{White socks} = \text{Total socks} - \text{Black socks} - \text{Blue socks} - \text{Red socks}
\][/tex]
[tex]\[
\text{White socks} = 100 - 24 - 19 - 12
\][/tex]
[tex]\[
\text{White socks} = 45
\][/tex]
Now, we need to find the number of socks that are not white. This will be the sum of the black, blue, and red socks:
[tex]\[
\text{Non-white socks} = \text{Total socks} - \text{White socks}
\][/tex]
[tex]\[
\text{Non-white socks} = 100 - 45
\][/tex]
[tex]\[
\text{Non-white socks} = 55
\][/tex]
Next, to find the probability that Malachi will not pick a white sock, we need to divide the number of non-white socks by the total number of socks:
[tex]\[
\text{Probability of picking a non-white sock} = \frac{\text{Non-white socks}}{\text{Total socks}}
\][/tex]
[tex]\[
\text{Probability} = \frac{55}{100}
\][/tex]
[tex]\[
\text{Probability} = \frac{11}{20}
\][/tex]
Therefore, the probability that Malachi will not pick a white sock is [tex]\(\frac{11}{20}\)[/tex].
The correct answer is [tex]\( \boxed{\frac{11}{20}} \)[/tex].
