Question

Question #00fa5

Answer 1

See explanation.

Explanation:

In this excercise the easiest way to calculate the probability of choosing different colours is to use the opposite even probability.

The opposite event is: Two balls of the same colour are drawn.

Its probability can be calculated as:

`P(SC)=P(R_1)*P(R_2)+P(W_1)*P(W_2)+P(B_1)*P(B_2)`

Where the events are:

`SC` - balls of the same colours are drawn

`R_1` - first ball is red
`R_2` - second ball is red

`W_1` - first ball is white
`W_2` - second ball is white

`B_1` - first ball is black
`B_2` - second ball is black

`P(SC)=10/20*9/19+5/20*4/19+5/20*4/19`

`P(SC)=(90+20+20)/380=130/380=13/38`

Now we can calculate

`DC` - the prbability of choosing different colours:

`P(DC)=1-P(SC)=1-13/38=25/38`

Answer: The probability of choosing balls of different colours is `25/38`.