Question

each day, stus probability of being on time to work is 0.4. each day is independent of the other days. what is the probability that stu will be on time this week on monday and tuesday?
ex: 0.005

Explanation:

Step1: Use the multiplication rule for independent events

Since the events (being on - time on Monday and being on - time on Tuesday) are independent, and the probability of being on - time each day is \(p = 0.4\).
The multiplication rule for independent events \(A\) and \(B\) is \(P(A\cap B)=P(A)\times P(B)\)

Step2: Calculate the probability

Let \(A\) be the event of being on - time on Monday and \(B\) be the event of being on - time on Tuesday.
We know that \(P(A) = 0.4\) and \(P(B)=0.4\)
Then \(P(A\cap B)=0.4\times0.4\)

$$0.4\times0.4=\frac{4}{10}\times\frac{4}{10}=\frac{16}{100}=0.16$$

Answer:

\(0.16\)