Answer:
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
[tex]\dfrac{5}{15}=\dfrac{1}{3},[/tex]
then the probability that all 3 marbles are blue is
[tex]\dfrac{1}{3}\times \dfrac{1}{3}\times \dfrac{1}{3}=\dfrac{1}{27}[/tex]
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
[tex]\dfrac{5}{15}\times \dfrac{4}{14}\times \dfrac{3}{13}=\dfrac{2}{91}[/tex]
