Question

An urn contains 3 red and 5 orange marbles. 2 marbles are selected without replacement. Find the probability that the second marble selected is orange given that the first marble selected is orange.

Answer 1

Answer:
`(5)/(14)`

Explanation:

Given: An urn contains 3 red and 5 orange marbles.

Total marbles = 3+5=8

Probability of getting orange marble =
`\frac{\text{Number of orange marble}}{\text{Total}}`

`=(5)/(8)`

Now marbles left = 7

Orange marbles left = 4

and Probability of getting orange marble =
`\frac47`

The probability that the second marble selected is orange given that the first marble selected is orange
`=\frac58*\frac47=(5)/(2)*\frac17=(5)/(14)`

Required probability=
`(5)/(14)`