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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
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
= 4×1 = 4
getting at most 1 defective battery = 60 + 36 + 4 = 100
Probability =