Question

There is a bag filled with 6 blue and 5 red marbles.

A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting 2 that are different in colour?

Answer 1

60/121

Explanation:

There are two outcomes that are included in the event "2 different in color" -- either Red followed by Blue (RB) or Blue followed by Red (BR).

Probability of RB is
`(5)/(11)* (6)/(11)=(30)/(121)` The denominator 11 does not change in the second fraction because you put the first marble back; still 11 marbles in the bag.

Probability of BR is
`(6)/(11) * (5)/(11)=(30)/(121)`

Probability of RB or BR: add the probabilities to get 60/121.