Probability

A small bag contains 6 black and 9 red pens of the same type. Two pens are taken at random one after the other without replacement. Calculate the probability that;

(a) one is black.

(b) both are of different colours.

A box contains identical buttons of different colours. There are 20 black, 12 red, and 4 white buttons in the box. Two buttons are picked at random one after the other and are not replaced in the box.

What is the probability that both buttons are white?

A box of chalk contains 5 white, 4 blue, and 3 yellow pieces of chalk. A piece of chalk is selected at random from the box and not replaced. A second piece of chalk is then selected.

Find the probability of selecting pieces of chalk that are of the same colour.

In a box of 10 bulbs, 3 are faulty. If two bulbs are drawn at random one after the other, find the probability that;

(a) both are good.

• $\frac{7}{15}$

• $\frac{11}{15}$

• $\frac{1}{15}$

• $\frac{3}{4}$

(b) one is faulty and the other is good.