suppose there 10 marbles in a bag and 3 of them are defective.Two marbles are to be selected one after the other without replacement.What is the probability of selecting a defective marble followed by another defective marble?

3/10 * 2/9

To find the probability of selecting a defective marble followed by another defective marble, we need to calculate the probability at each step.

Step 1: Probability of selecting a defective marble in the first draw:
There are initially 10 marbles in the bag, out of which 3 are defective. Therefore, the probability of selecting a defective marble in the first draw is 3/10.

Step 2: Probability of selecting a defective marble in the second draw:
After the first marble is drawn, there are now 9 marbles left in the bag, with 2 defective marbles. Therefore, the probability of selecting a defective marble in the second draw is 2/9.

To find the overall probability of both events happening (selecting a defective marble followed by another defective marble), we need to multiply the probabilities together since both events need to occur:

Probability = (3/10) * (2/9) = 6/90 = 1/15

Therefore, the probability of selecting a defective marble followed by another defective marble is 1/15.