Question

Given the following probabilities for choosing 2 marbles from a bag of 10 marbles, determine if the events are dependent or independent.

P(blue) = , P(green) = , and P(blue and green) =

dependent, because the product of P(blue) and P(green) does not equal P(blue and green)
dependent, because the product of P(blue) and P(green) equals P(blue and green)
independent, because the product of P(blue) and P(green) does not equal P(blue and green)
independent, because the product of P(blue) and P(green) equals P(blue and green)

Answer 1

Dependent, because the product of P(blue) and P(green) does not equal P(blue and green).

Reason: drawing two marbles from the bag without replacement makes the second draw depend on the first, so P(blue and green) ≠ P(blue)·P(green). (If draws were with replacement the events would be independent.)