EventProbability
Too much enamel0.27
Too little enamel0.2
Uneven application0.35
No defects noted0.43
(1) What is the probability of a paint defect?
(2) What is the probability of a paint defect which includes an
improper amount of paint?
(3) What is the probability of a paint defect which results from
an improper amount of paint and uneven application?
(4) What is the probability of a paint defect which results from
the proper amount of paint, but uneven application?
I would love to answer those questions, but be warned, my answers might be a little clowny! So here we go:
(1) What is the probability of a paint defect?
Based on the given information, the probability of a paint defect is 1. But don't worry, you can always paint over it!
(2) What is the probability of a paint defect which includes an improper amount of paint?
Well, the probability of a paint defect due to an improper amount of paint is 0.2. That's not too bad, I mean, it's not perfect, but it's not a masterpiece either!
(3) What is the probability of a paint defect which results from an improper amount of paint and uneven application?
The probability of such a paint defect is 0.35. It's like trying to create a work of art while riding a unicycle - things might get messy!
(4) What is the probability of a paint defect which results from the proper amount of paint, but uneven application?
Ah, the probability of this paint defect is 0. The application might be uneven, but hey, at least you got the right amount of paint! Not too shabby, I must say!
To calculate the probabilities of the various paint defects, we need to understand how to combine probabilities in different scenarios.
First, let's define the events:
A: Too much enamel (probability = 0.27)
B: Too little enamel (probability = 0.2)
C: Uneven application (probability = 0.35)
D: No defects noted (probability = 0.43)
Now let's answer each of the questions:
(1) What is the probability of a paint defect?
To calculate the probability of a defect, you need to sum the probabilities of the individual defect events. In this case, all the events represent defects except event D (no defects noted). So, the probability of a paint defect is the sum of the individual probabilities: P(A) + P(B) + P(C).
Substituting the values: 0.27 + 0.2 + 0.35 = 0.82
Therefore, the probability of a paint defect is 0.82.
(2) What is the probability of a paint defect which includes an improper amount of paint?
Here, we are interested in the probability of events A or B. Since these events are mutually exclusive (a paint defect cannot have both too much and too little enamel), we can simply add their individual probabilities.
P(A or B) = P(A) + P(B)
Substituting the values: 0.27 + 0.2 = 0.47
Therefore, the probability of a paint defect which includes an improper amount of paint is 0.47.
(3) What is the probability of a paint defect which results from an improper amount of paint and uneven application?
To calculate the probability of both events A and C occurring, we need to multiply their probabilities together.
P(A and C) = P(A) * P(C)
Substituting the values: 0.27 * 0.35 = 0.0945
Therefore, the probability of a paint defect resulting from an improper amount of paint and uneven application is approximately 0.0945.
(4) What is the probability of a paint defect which results from the proper amount of paint, but uneven application?
For this scenario, we are interested in event C occurring given that event A did not occur (no too much enamel). We can calculate this by multiplying the probability of event C by the complementary probability (1 - P(A)).
P(C | not A) = P(C) * (1 - P(A))
Substituting the values: 0.35 * (1 - 0.27) = 0.35 * 0.73 = 0.2555
Therefore, the probability of a paint defect which results from the proper amount of paint but uneven application is approximately 0.2555.