A cartoon contains 20 bulbs, 5 of which are defective. Find the probability that if a sample of 3 bulbs is chosen at random from the cartoon 2 will be defective.

A factory has two machines A and B. Past record shows that machine A produced 60% of items of output and machine B produced 40% of items. Further, 2% of items, produced by machine A and 1% produced by machine B were defective. All the items are put into a stockpile and then one item is chosen at random from this and this is found to be defective. What is the probability that it was produced by machine B?

A lot contains 15 items of which 5 are defective. If three items are drawn at random, find the probability that (i) all three are defective

It is known that 10% of certain articles manufactured are defective, what is the probability that in a random sample of 12 such articles 9 are defective?

A lot contains 15 items of which 5 are defective. If three items are drawn at random, find the probability that none of the three is defective. Do this problem directly.

From a lot of 15 bulbs which include 5 defectives, a sample of 2 bulbs is drawn at random (without replacement). Find the probability distribution of the number of defective bulbs.

From a lot of 15 bulbs which include 5 defectives, a sample of 4 bulbs is drawn one by one with replacement. Find the probability distribution of number of defective bulbs. Also, find the mean of the distribution.

In a bulb factory, machines A, B and C manufacture 60%, 30% and 10% bulbs, respectively. 1%, 2% and 3% of the bulbs produced, respectively by A, B and Care found to be defective. A bulb is picked up at random from the total production and found to be defective. Find the probability that this bulb was produced by machine A.

From a bag containing 5 black and 7 white balls, 3 balls are drawn in succession . Find the probability that all three are of the same colour.