Question

There is a bag filled with 3 blue and 5 red marbles.

A marble is taken at random from the bag, the colour is noted and then it is not replaced.
Another marble is taken at random.
What is the probability of getting 2 that are different in colour?

Answer 1

15/28 is the probability of getting 2 that are different in colour.

Explanation:

• 3 blue and 5 red marbles

He is going to pick any marble, in second try, it must be a different colour marble.

total marble: 3 + 5 = 8 marbles

For blue marble:

In first try for blue marble: 3/8

• total marble will decrease by 1, 7 marbles.

second try for red marble: 5/7

probability then: 5/7 * 3/8 = 15/56 is the probability for blue marble.

For red marble:

In first try for red marble: 5/8

• total marble will decrease by 1, 7 marbles.

second try for blue marble: 3/7

probability then: 5/8 * 3/7 = 15/56

**

total probability of getting different in colour:

15/56 + 15/56

15/28 **

Answer 2

• 15/28

Explanation:

There are 3 blue, 5 red and the total of 8 marbles.

Two different colored marbles are:

• blue, then red or red, then blue

Find the probability of each case:

• P(b, r) = 3/8*5/7 = 15/56
• P(r, b) = 5/8*3/7 = 15/56

Required probability is:

• P(different color) = 15/56*2 = 15/28