Question

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

Answer 1

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

$\dfrac{5}{15}=\dfrac{1}{3},$

then the probability that all 3 marbles are blue is

$\dfrac{1}{3}\times \dfrac{1}{3}\times \dfrac{1}{3}=\dfrac{1}{27}$

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

$\dfrac{5}{15}\times \dfrac{4}{14}\times \dfrac{3}{13}=\dfrac{2}{91}$