Question

a bag contains 3 red marbles and 4 white marbles. two marbles are drawn in succession without replacement. find the probabilities of the following events: 1. the first marble drawn is red and the second is white. answer: 0.2449 2. both marbles drawn are red.

Answer 1

1. 0.2857

2. 0.1429

Explanation:

In probability:
AND = multiplication

OR = addition

There are total seven marbles. However, when the first marble is drawn, it is NOT replaced.

There are:

3 red

4 White

1. When First marble is RED AND second marble is WHITE:

=
`(3)/(7).(4)/(6)`

=
`(12)/(42)`

Divide both the numerator and denominator by the Highest Common Factor ‘6’:

=
`(2)/(7)`

= 0.2857 (Rounded off to 4 significant figures)

2. When First marble is RED AND second marble is RED:

`= (3)/(7) .(2)/(6)`

`= (6)/(42)`

Divide both the numerator and denominator by the Highest Common Factor ‘6’:

`= (1)/(7)`

`= 0.1429` (Rounded off to 4 significant figures)