Question

in ms. smith's class, each student averages one day absent out of thirty. what is the probability that out of any two students chosen at random, one student will be absent while the other is present? express your answer as a percent rounded to the nearest tenth.

Answer 1

The probability that out of any two students chosen at random, one student will be absent while the other is present in Ms. Smith's class is approximately 6.4%.

Step-by-step explanation:

In Ms. Smith's class, the probability of each student being absent is 1 out of 30. When choosing any two students at random, we want to calculate the probability that one student is absent while the other is present. To solve this problem, we consider two scenarios—Student A is absent and Student B is present, or Student A is present and Student B is absent—and then we add these probabilities together.

The probability of Student A being absent is 1/30, and the probability of Student B being present is 29/30. Conversely, the probability of Student A being present is 29/30, and the probability of Student B being absent is 1/30. Hence, the total probability is:

(1/30) × (29/30) + (29/30) × (1/30)

This simplifies to:

2 × (1/30) × (29/30)

And when calculated, it gives:

2 × 1/30 × 29/30 = 58/900

Converted to a percentage, this is approximately:

(58/900) × 100 ≈ 6.4%

This is the probability that out of any two students chosen at random, one will be absent while the other is present, rounded to the nearest tenth as a percent.