Answer:
a.) 0.5
b.) 0.66
c.) 0.83
Step-by-step explanation:
As given, 
Total Number of Batteries in the drawer = 10
Total Number of defective Batteries in the drawer = 4
⇒Total Number of non - defective Batteries in the drawer = 10 - 4 = 6
Now,
As, a sample of 3 is taken at random without replacement.
a.)
Getting exactly one defective battery means -
1 - from defective battery
2 - from non-defective battery
So, 
Getting exactly 1 defective battery = ⁴C₁ × ⁶C₂ =   ×
 × 
                                                                             =  ×
 × 
                                                                             =  ×
 × 
                                                                             =  ×
 × 
                                                                             =  ×
 ×  = 60
 = 60
Total Number of possibility = ¹⁰C₃ = 
                                                         = 
                                                         = 
                                                         = 
                                                         = 120
So, probability = 
b.)
at most one defective battery :
⇒either the defective battery is 1 or 0
If the defective battery is 1 , then 2 non defective 
Possibility  = ⁴C₁ × ⁶C₂ = 60
If the defective battery is 0 , then 3 non defective 
Possibility   = ⁴C₀ × ⁶C₃ 
                    =   ×
 × 
                    =  ×
 × 
                    = 1 × 
                    = 1× 
                    = 1 × 20 = 20
getting at most 1 defective battery = 60 + 20 = 80
Probability = 
c.)
at least one defective battery :
⇒either the defective battery is 1 or 2 or 3
If the defective battery is 1 , then 2 non defective 
Possibility  = ⁴C₁ × ⁶C₂ = 60
If the defective battery is 2 , then 1 non defective 
Possibility   = ⁴C₂ × ⁶C₁ 
                    =   ×
 × 
                    =  ×
 × 
                    =  ×
 × 
                    =  ×
 × 
                    = 6 × 6 = 36
If the defective battery is 3 , then 0 non defective 
Possibility   = ⁴C₃ × ⁶C₀ 
                    =   ×
 × 
                    =  ×
 × 
                    =  × 1
 × 1
                    = 4×1 = 4
getting at most 1 defective battery = 60 + 36 + 4 = 100
Probability = 