A product is assembled from 3 components X,Y,Z and the probability of these components being defective is 0.01, 0.02,0.05. i have to find the probability that the assumed product will not be defective?
can someone explain to me, how do it? thanks
To find the probability that the assumed product will not be defective, you need to find the probability that all three components are not defective. This can be done by multiplying the probabilities of each component not being defective.
Given that the probability of component X being defective is 0.01, the probability of it not being defective is 1 - 0.01 = 0.99.
Similarly, the probability of component Y not being defective is 1 - 0.02 = 0.98, and the probability of component Z not being defective is 1 - 0.05 = 0.95.
To find the probability that all three components are not defective, you need to multiply these probabilities together:
0.99 * 0.98 * 0.95 = 0.921.
Therefore, the probability that the assumed product will not be defective is 0.921, or approximately 92.1%.
To find the probability that the assumed product will not be defective, you need to consider the probability that each component is not defective and then use the probability multiplication rule.
Let's first calculate the probability that each component is not defective:
- The probability that component X is not defective is 1 - 0.01 = 0.99.
- The probability that component Y is not defective is 1 - 0.02 = 0.98.
- The probability that component Z is not defective is 1 - 0.05 = 0.95.
Now, we can use the probability multiplication rule:
- Multiply the probabilities of each component not being defective.
P(not defective) = P(X not defective) x P(Y not defective) x P(Z not defective)
P(not defective) = 0.99 x 0.98 x 0.95
Finally, calculate the result:
- P(not defective) = 0.99 x 0.98 x 0.95 = 0.92103
Therefore, the probability that the assumed product will not be defective is approximately 0.92103, or 92.103%.