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: $\dfrac{5}{14}$

Step-by-step explanation:

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

Total marbles = 3+5=8

Probability of getting orange marble = $\dfrac{\text{Number of orange marble}}{\text{Total}}$

$=\dfrac{5}{8}$

Now marbles left = 7

Orange marbles left = 4

and Probability of getting orange marble = $\dfrac47$

The probability that the second marble selected is orange given that the first marble selected is orange$=\dfrac58\times\dfrac47=\dfrac{5}{2}\times\dfrac17=\dfrac{5}{14}$

Required probability= $\dfrac{5}{14}$