Question

4.) A bag contains 10 red marbles and 5 blue marbles. You randomly select 3 marbles from the bag. What is

the probability that all 3 marbles are blue when (a) you replace each marble before selecting the next one and
(b) you do not replace each marble before selecting the next one?​

Answer 1

To find the probability of drawing three blue marbles, we need to consider two scenarios: replacing each marble before selecting the next one and not replacing each marble before selecting the next one.

Step-by-step explanation:

To find the probability that all three marbles drawn are blue, we need to consider two scenarios:

Scenario 1: When we replace each marble before selecting the next one:

In this scenario, the probability of drawing a blue marble on each draw remains the same. Therefore, the probability of drawing three blue marbles in this scenario is:

P(Blue on 1st draw) * P(Blue on 2nd draw) * P(Blue on 3rd draw) =

*

Scenario 2: When we do not replace each marble before selecting the next one:

In this scenario, the probability of drawing a blue marble changes with each draw. Therefore, the probability of drawing three blue marbles in this scenario is:

P(Blue on 1st draw) * P(Blue on 2nd draw) * P(Blue on 3rd draw) =

*

Answer 2

a) 1/27

b) 2/91

Step-by-step explanation:

A bag contains 10 red marbles and 5 blue marbles (15 marbles in total). You randomly select 3 marbles from the bag.

a) You replace each marble before selecting the next one.

The probability of selecting one blue marble is

`(5)/(15)=(1)/(3),`

then the probability that all 3 marbles are blue is

`(1)/(3)* (1)/(3)* (1)/(3)=(1)/(27)`

b) You do not replace each marble before selecting the next one. Each time the number of blue marbles decreases by 1 and the total number of marbles decreases by 1 too. So the probability that all 3 marbles are blue is

`(5)/(15)* (4)/(14)* (3)/(13)=(2)/(91)`