Question

A bag contains 3 black balls, 7 white balls, 6 black cubes, and 14 white cubes. Find the probability of drawing a ball and a black object

Answer 1

We have 3+7+6+14=30 objects.

We can select the first object in 30 ways, the second one in 29 ways.

So, there are $30\times 29=870$ possibilities.

There are 3+6=9 black objects and 7+14=21 white objects.

The first object must be a ball.

If it is white ball, then the second object must be one of the 9 black objects. There are $7\times 9=63$ possibilities.

If it is black ball, then the second object must one of the rest 8 black objects. There are$3\times 8=24$ possibilities.

So, probability is equal to $\frac{63+24}{870}=\frac{87}{870}=0.1$

Answer: 0.1