Question

Workplace accidents are categorized in three groups: minor, moderate and severe. The probability that a given accident is minor is 0.5, that it is moderate is 0.4, and that it is severe is 0.1. Two accidents occur independently in one month. Calculate the probability that neither accident is severe and at most one is moderate.

1) 0.25
2) 0.40
3) 0.45
4) 0.56
5) 0.65

Answer 1

To calculate the probability that neither accident is severe and at most one is moderate, we sum the probability of both accidents being minor and the probability of one accident being minor and the other moderate. The total probability is 0.65, making option 5 the correct answer.

Step-by-step explanation:

The student has asked to calculate the probability that neither accident is severe and at most one is moderate, given two independent accidents. We can use the given probabilities for minor, moderate, and severe accidents to calculate this probability. The possible outcomes that satisfy the condition are: both accidents are minor (M-M), one is minor and one is moderate (M-Md or Md-M), but not both moderate or a moderate and a severe.

• Probability of both accidents being minor: 0.5 (for minor) × 0.5 (for minor) = 0.25
• Probability of one minor and one moderate accident (either way around): 0.5 (for minor) × 0.4 (for moderate) = 0.20, and since it can occur in two different ways (minor then moderate or moderate then minor), we multiply by 2 to get 0.40.

The total probability is the sum of these independent probabilities, which is 0.25 + 0.40 = 0.65. Therefore, the correct answer is option 5) 0.65.