To determine the probability that Stu will be on time on Monday, Tuesday, and Wednesday, we need to consider a few key points:
1. Probability on any given day: Stu's probability of being on time on any given day is 0.3.
2. Independence of events: Each day's probability is independent of the other days.
Given these points, we can calculate the probability for each day individually and then combine them. Specifically, since events are independent, the probability that Stu will be on time on multiple days is found by multiplying the individual probabilities for each of those days.
- Probability of being on time on Monday: [tex]\(0.3\)[/tex]
- Probability of being on time on Tuesday: [tex]\(0.3\)[/tex]
- Probability of being on time on Wednesday: [tex]\(0.3\)[/tex]
Since each day is independent, the combined probability is the product of the probabilities:
[tex]\[
0.3 \times 0.3 \times 0.3 = 0.027
\][/tex]
Thus, the probability that Stu will be on time this week on Monday, Tuesday, and Wednesday is [tex]\(0.027\)[/tex].
