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Answer:
a. 1365 ways
b. Probability = 0.4096
c. Probability = 0.5904
Explanation:
Given
PCs = 15
Purchase = 3
Solving (a): Ways to select 4 computers out of 15, we make use of Combination formula as follows;
Where
<em>Hence, there are 1365 ways </em>
Solving (b): The probability that exactly 1 will be defective (from the selected 4)
First, we calculate the probability of a PC being defective (p) and probability of a PC not being defective (q)
<em>From the given parameters; 3 out of 15 is detective;</em>
So;
Solving further using binomial;
Where n = 4
For the probability that exactly 1 out of 4 will be defective, we make use of
Substitute 4 for n, 0.2 for p and 0.8 for q
Solving (c): Probability that at least one is defective;
In probability, opposite probability sums to 1;
Hence;
<em>Probability that at least one is defective + Probability that at none is defective = 1</em>
Probability that none is defective is calculated as thus;
Substitute 4 for n and 0.8 for q
Substitute 0.4096 for Probability that at none is defective
Probability that at least one is defective + 0.4096= 1
Collect Like Terms
Probability = 1 - 0.4096
Probability = 0.5904