Question

Please answer 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 exactly 1 blue?

Answer 1

`(15)/(28)` is the required probability.

Explanation:

Total number of Marbles = Blue + Red
`= 3 + 5 = 8`

Probability of getting blue
`= (3)/(8)`

Probability of not getting a blue
`=(5)/(8)`

To get exactly one blue in two draws, we either get a blue, not blue, or a not blue, blue.

First Draw Blue, Second Draw Not Blue:

1st Draw:
`P(Blue) = (3)/(8)`

2nd Draw:
`P(Not\:Blue)=(5)/(7)` (since we did not replace the first marble)

To get the probability of the event, since each draw is independent, we multiply both probabilities.

`P(Event)=(3)/(8)\cdot (5)/(7)=(15)/(56)`

First Draw Not Blue, Second Draw Not Blue:

1st Draw:
`P(Not\:Blue)=(5)/(8)`

2nd Draw:
`P(Not\:Blue)=(3)/(7)` (since we did not replace the first marble)

To get the probability of the event, since each draw is independent, we multiply both probabilities.

`P(Event)=(5)/(8)\cdot (3)/(7)=(15)/(56)`

To get the probability of exactly one blue, we add both of the events:

`(15)/(56)+(15)/(56)=(15)/(28)`