Question

An urn contains 6 balls of which two are red and four are black. Two balls are drawn at random. Probability that they are of the different colours is
(a) 2 / 5 (b) 1 /15 (c) 8 / 15 (d) 4 /15

Answer 1

8/15

Explanation:

Total Number of Balls = 6

Probability of getting 2 balls of Different colors = 2C1 x 4C1 / 6C2

                                                                              = 2 x 4 / 15

                                                                              = 8/15  Answer

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Answer 2

Total number of balls = 6 (Given)

Number of red balls = 2 (Given)

Number of black balls = 4 (Given)

Number of balls drawn at random = 2 (Given)

Let = P ( they are of different colours)  

= P ( first ball drawn is black) × P ( second ball drawn is black) + P( first ball drawn is red) × P ( second ball drawn is black)

= 4/6 × 2/5 + 2/6 × 4/5

= 8/30 + 8/30

= 16/30

= 8/15

Therefore, the probability that they are of the different colours is 8/15