Let's solve the problem step-by-step.
First, we need to sum up the probabilities of the algorithm choosing any of the weekdays (Monday, Tuesday, Wednesday, Thursday, and Friday). According to the given table:
- Probability of choosing Monday: 0.12
- Probability of choosing Tuesday: 0.07
- Probability of choosing Wednesday: 0.05
- Probability of choosing Thursday: 0.28
- Probability of choosing Friday: 0.15
To find the total probability of selecting a weekday, we sum these probabilities:
[tex]\[
\text{Total probability of choosing a weekday} = 0.12 + 0.07 + 0.05 + 0.28 + 0.15 = 0.67
\][/tex]
Next, we need to find the probability that the algorithm will not choose one of the weekdays.
Since the total probability of choosing any day from the week must add up to 1, the probability of not choosing a weekday is:
[tex]\[
\text{Probability of not choosing a weekday} = 1 - \text{Probability of choosing a weekday}
\][/tex]
Using the calculated total probability of choosing a weekday:
[tex]\[
\text{Probability of not choosing a weekday} = 1 - 0.67 = 0.33
\][/tex]
So, the probability that the algorithm will not choose one of the weekdays is:
[tex]\[
\boxed{0.33}
\][/tex]
