A quality control engineer inspects a shipment of 25 solar panels, of which 9 are premium grade and 16 are standard grade. The engineer randomly selects 2 panels from the shipment, one after another without replacement. What is the probability, expressed as a decimal, that at least one of the two selected panels is premium grade?
Answer: 0.6
Answer
The probability that at least one of the two selected panels is premium grade is 0.6.
Selection without replacement creates dependent events because the outcome of the first draw alters the pool available for the second draw. Out of 25 panels, 16 are standard grade. The probability that the first drawn panel is standard grade is 16/25. If the first panel is standard grade, 15 standard panels remain out of 24 total panels, giving a probability of 15/24 for the second draw. The probability of selecting two standard panels is (16/25) × (15/24) = 0.40. Using complementary probability, the probability that at least one panel is premium grade is 1 - 0.40 = 0.60.
Step-by-Step Solution
Key Concept
Dependent Events and Complementary Probability
Alternative Method
Sum the probabilities of mutually exclusive favorable outcomes: P(1st premium, 2nd standard) + P(1st standard, 2nd premium) + P(both premium) = (9/25)(16/24) + (16/25)(9/24) + (9/25)(8/24) = 0.24 + 0.24 + 0.12 = 0.60.
Estimated Time:1m 30s