Final answer:
The question seems related to statistical concepts involving correlation coefficients and the probability of independent events in a high school mathematics context. Correlation coefficient -0.90 indicates a stronger negative relationship compared to -0.50. The probability of independent events A and B occurring together, P(A AND B), is found by multiplying their individual probabilities, resulting in 0.06 for P(A) = 0.2 and P(B) = 0.3.
Step-by-step explanation:
The given prompt appears to be dealing with a statistical concept, likely related to correlation coefficients, probabilities, or linear equations. The list of numbers provided along with α (alpha) levels and P(A and B) probabilities suggests these are high school level statistical problems.
For instance, the problem mentioning correlation coefficients discusses the strength of relationship between two variables, and the options given seem to be asking the student to identify the strongest coefficient. In this context, option A. -0.90 indicates a very strong negative correlation, stronger than -0.50, which means as one variable increases, the other variable decreases.
For the question involving the possibility of independent events A and B, the formula for the probability of both independent events occurring is P(A AND B) = P(A) * P(B). Since P(A) = 0.2 and P(B) = 0.3, multiplying these gives P(A AND B) = 0.06, making D. .06 the correct choice.
Without the full context of the prompt, providing a conclusive answer to the original question is not possible. However, these explanations give a good understanding of how to approach similar statistical problems, specifically dealing with correlation coefficients and probabilities of independent events.