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Answer:
(a) The probability that at least one of these components will need repair within 1 year is 0.0278.
(b) The probability that exactly one of these component will need repair within 1 year is 0.0277.
Step-by-step explanation:
Denote the events as follows:
<em>A</em> = video components need repair within 1 year
<em>B</em> = electronic components need repair within 1 year
<em>C</em> = audio components need repair within 1 year
The information provided is:
P (A) = 0.02
P (B) = 0.007
P (C) = 0.001
The events <em>A</em>, <em>B</em> and <em>C</em> are independent.
(a)
Compute the probability that at least one of these components will need repair within 1 year as follows:
P (At least 1 component needs repair)
= 1 - P (No component needs repair)
Thus, the probability that at least one of these components will need repair within 1 year is 0.0278.
(b)
Compute the probability that exactly one of these component will need repair within 1 year as follows:
P (Exactly 1 component needs repair)
= P (A or B or C)
Thus, the probability that exactly one of these component will need repair within 1 year is 0.0277.