Question

1. An urn contains two red, one purple, and two green marbles. Two marbles are randomly drawn in succession without replacement. Determine the probability that the first marble is green and the second is red.

2. An urn contains two red, two purple, and two green marbles. Two marbles are randomly drawn in succession without replacement. Determine the probability that both marbles are red.

Answer 1

1.

Draw 1: Green

Red: 2

Purple = 1

Green= 2

Total marbles = 5

P(Draw 1: Green) = 2/5 = 0.4

Draw 2: Red

Red: 2

Purple = 1

Green= 1

Total marbles = 4

P(Draw 2: Red) = 2/4 = 0.5

So,

the probability that the first marble is green and the second is red. = 0.4 X 0.5 =0.2

So,

Answer is:

0.2

2.

Draw 1: Red

Red: 2

Purple = 1

Green= 2

Total marbles = 5

P(Draw 1: Red) = 2/5 = 0.4

Draw 2: Red

Red: 1

Purple = 1

Green= 2

Total marbles = 4

P(Draw 2: Red) = 1/4 = 0.25

So,

the probability that both marbles are red. = 0.4 X 0.25 = 0.1

So,

Answer is:

0.1