Question

a bag contains red and blue marbles. you draw one marble, note its color, and put it back. then you draw again. why are these two draws independent events? because youre looking for the same colors both times because youre drawing from the same bag both times because the outcome of the first draw doesnt change the probability for the second draw because marbles are physical objects two events a and b are complementary. if p(a) = 0.35, what can you conclude about these events? p(b) = 1.35 because probabilities can exceed 1 p(b) = 0.65 and a and b cannot happen at the same time p(b) = 0.65 and a and b can happen together p(b) = 0.35 and they are independent

Explanation:

1. For the first question, independent events are defined as events where the outcome of one event does not affect the probability of the other event. Since the marble is replaced after the first draw, the composition of marbles in the bag remains the same for the second draw, so the first - draw outcome doesn't change the second - draw probability.
2. For the second question, if two events A and B are complementary, the sum of their probabilities is 1 (i.e., \(P(A)+P(B) = 1\)). Given \(P(A)=0.35\), then \(P(B)=1 - P(A)=1 - 0.35 = 0.65\). Also, complementary events cannot occur simultaneously.

Answer:

1. Because the outcome of the first draw doesn't change the probability for the second draw
2. \(P(B)=0.65\) and A and B cannot happen at the same time