Question

The probability that a student enrolled at a local high school will be absent on a particular day is 0.05, assuming that the student was in attendance the previous school day. However, if a student is absent, the probability that they will be absent again the following day is 0.14. Assume that the student was in attendance the previous day.
What is the probability that a student will be absent 3 days in a row?

Answer 1

To calculate the probability that a student will be absent 3 days in a row, we can use the conditional probability formula:

P(absent on Day 1) * P(absent on Day 2 | absent on Day 1) * P(absent on Day 3 | absent on Day 2)

P(absent on Day 1) = 0.05 (given)
P(absent on Day 2 | absent on Day 1) = 0.14 (given)
P(absent on Day 3 | absent on Day 2) = 0.14 (given)

So, the probability that a student will be absent 3 days in a row is:
0.05 * 0.14 * 0.14 = 0.00098

Therefore, the probability that a student will be absent 3 days in a row is 0.00098 or 0.098%.