Answer to Question #162403 in Statistics and Probability for Ben Harwood

Question

There is a bag filled with 5 blue and 4 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 at least 1 blue?

Answer 1

$\text{total number of marbles }5+4=9$

$\text{the probability of get a red marble } p_1=\frac{4}{9}$

$\text{the same probability and on the second try}$

$\text{so the ball is replaced } p_2=\frac{4}{9}$

$\text{the probability of get both red balls }$

$\text{out of two attempts } p=p_1*p_2=\frac{16}{81}$

$\text{events get 2 red balls and get at least one blue ball are incompatible}$

$\text{the probability of getting at least 1 blue:}$

$1-p=1-\frac{16}{81}=\frac{65}{81}$

Answer: $\frac{65}{81}$