Question

A basket contains 50 nuts. Given that 5 nuts are defective (denoted by D) and the rest are good (denoted by d) use a tree diagram to display the values when 2 nuts are drawn from this basket without replacement.

Hence

A) find (d/D)

B) find P (both are defective)

C) Find P (no defective)using the compliment law only

Answer 1

Let

D1 : event that first nut drawn is defective    
d1 : event that first nut drawn is not defective    
D2 : event that second nut drawn is defective    
d2 : event that second nut drawn is not defective    

Tree Diagram

A) P(d | D)        
That is to find P(second nut is not defective | first nut is defective)        
P(d | D) = P(d2 | D1)        
From the tree diagram we can see that P(d2 | D1)

P(d | D)        

         
P(d | D) = 0.9184    
         

B) P(both are defective)        
         
= P(D1 AND D2)

         
         
= 0.0082        
P(both are defective) = 0.0082        
         

C) P(both are not defective)        
P(both are not defective) = 1 - P(atleast one is defective)                           (… Complement Law)   
   = 1 - [P(d1 AND D2) + P(D1 AND d2) + P(D1 and D2)]        

= 0.8082        
P(both are not defective) = 0.8082