Question

A box contains 8 green light bulbs of which 3 are defective. It also contains 12 red light bulbs of which 5 are defective. A bulb is chosen at random from the box

Is choosing a red bulb and choosing a defective bulb independent? explain.

Answer 1

@Hero @Nnesha

Answer 2

Let \(R\) = red and let \(D\) = defective. To know if you have independent events, you need to verify if this is true:
\(P(R \cap D)=P(R)P(D)\) . If both sides are equal, then the events are independent.

So, is the probability of being (red AND defective simultaneously; i.e. \(P(R \cap D)\)), the same as the product of the probability of being red , \(P(R)\), and of being defective, \(P(D)\).