Question

A bag contains 10 red marbles, 15 yellow marbles, 5 green marbles, and 20 blue marbles. Five marbles are drawn from the bag. what is the aproximate probability that exactly two of the five are blue?

Answer 1

To determine the probability that exactly two of the five marbles are blue, we will use the rule of multiplication. 

Let event A = the event that the first marble drawn is blue; and let B = the event that the second marble drawn is blue. 
To start, it is given that there are 50 marbles, 20 of them are blue.  Therefore, P(A) = 20/50
After the first selection, there are 49 marbles left, 19 of them are blue. Therefore, P(A|B) = 19/49
Based on the rule of multiplication:P(A ∩ B) = P(A)*P(A|B)P(A ∩ B) =  (20/50) (19/49)P(A ∩ B) = 380/2450P(A ∩ B) = 38/245 or 15.51%

The probability that there will be two blue marbles among the five drawn marbles is 38/245 or 15.51%

We got the 15.51% by dividing 38 by 245. The quotient will be 0.1551. We then multiplied it by 100% resulting to 15.51%