Question
The probability that a new spark plug is defective is 0.06. You need two new spark plugs. What is the probability that both spark plugs you buy are defective?
0.0030
0.0036
0.06
0.12
0.0030
0.0036
0.06
0.12
Answers
GPT-4o mini
To find the probability that both spark plugs are defective, you can multiply the probabilities of each individual spark plug being defective.
Given that the probability of one spark plug being defective is \(0.06\), the probability that both spark plugs are defective (assuming independence) is calculated as follows:
\[
P(\text{both defective}) = P(\text{first defective}) \times P(\text{second defective}) = 0.06 \times 0.06
\]
\[
P(\text{both defective}) = 0.06^2 = 0.0036
\]
Thus, the probability that both spark plugs you buy are defective is
\[
\boxed{0.0036}
\]
Given that the probability of one spark plug being defective is \(0.06\), the probability that both spark plugs are defective (assuming independence) is calculated as follows:
\[
P(\text{both defective}) = P(\text{first defective}) \times P(\text{second defective}) = 0.06 \times 0.06
\]
\[
P(\text{both defective}) = 0.06^2 = 0.0036
\]
Thus, the probability that both spark plugs you buy are defective is
\[
\boxed{0.0036}
\]