Help with a probability problem?

Question

Event Probability
Too much enamel 0.25
Too little enamel 0.21
Uneven application0.32
No defects noted 0.46

(1) What is the probability of a paint defect? .54

(2) What is the probability of a paint defect which includes an improper amount of paint? .46

(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 got the first two but have no idea how to do the last two problems. I keep getting those wrong. PLEASE HELLLLPPP
thanks in advance

none of u were right

joe c was correct thanks

Answer 1

I agree with bandf but think he has (3) and (4) reversed.

I think (3) = ((0.25 + 0.21) + 0.32) - 0.54 = 0.24
I think (4) = 0.54 - 0.25 - 0.21 = 0.08

Too much and too little enamel (improper amt) are mutually exclusive. But obviously uneven application can overlap with improper amt because,
0.25+0.21+0.32 = 0.78 > 0.54.
The excess is 0.24 which represents uneven application and improper amount.

Total defects are 0.54, and improper qty is 0.46, so the difference, 0.08, represents uneven amt only.

Answer 2

You could draw a Venn diagram... the 'uneven application' event could happen both with or without other defects, so it overlaps.

You've figured out #1 and #2 correctly.

Since you know that any paint defect happens 54% (0.54) of the time, and the too much/too little defects happen 46% (0.46) that means that a paint defect that is both too much or too little and uneven application happens 8% of the time.
#3 = 0.08

That means that uneven application without a paint defect is 32% (0.32) minus 8% (0.08) = 24%
#4 = 0.24

CORRECTION:

As pointed out by Joe C, I should reverse my numbers, for #3 and #4.

Draw a Venn diagram.
The full area is 100%.
The improper paint areas are represented by two non-overlapping regions of 25% and 21% respectively. You can just put this into a single region of 46% with a dotted line through it representing too much and two little.
Then the uneven application is 32% and overlaps this region.

#1 - Probability of a paint defect is 1 - P(no defects). This is just 1 - 0.46 = 0.54 (54%)

#2 - Probabily of improper amounts of paint is P(too much enamel) + P(too little enamel) = 0.25 + 0.21 = 0.46 (46%).

#3 - Probability of a paint defect from *improper* amounts of paint *AND* uneven application. This is the overlap area. Since the outside (no defects) is 46% and the improper amount of paint (whether uneven or not) is 46%, that leaves 0.08 (8%) for the *proper* paint but uneven region. That means the overlap is 0.32 - 0.08 = 0.24. So the probability is 0.24 (24%).

#4 - Probabiliy of a paint defect which results from *proper* amounts of paint and uneven application. Like I stated above, this is the part of the uneven region that doesn't overlap. This is 1 - 0.46 - 0.46 = 0.08. So the probability is 0.08 (8%).

The asker said all the answers were wrong, so can you tell us what you think the answers are supposed to be???

Answer 3

When dealing with probabilities, remember that if the question says OR the you add probabilities and if it says AND you multiply probabilities. It sometimes helps to re-phrase the question.

2 becomes: What is the probability of a paint defect which includes an too much OR too little paint?

3 becomes: What is the probability of a paint defect which results from too much OR too little paint AND uneven application?

(0.25 + 0.21) * 0.32 = 0.147

4 becomes: What is the probability of a paint defect which results from the proper amount of paint AND uneven application?

We get the probability of the correct amount of paint by subtracting the probability of the incorrect amount from 1 hence the answer is

(1 - 0.46) * 0.32 = 0.1728

Answer 4

3. Multiply .46 (prob. of improper amount of paint) with .32 (prob. of uneven application) = .1472

4. 1 - .46 (from question 2) = .54, the probability of a proper amount of paint. Therefore, .54 times .32 (prob. of uneven application) = .1728, the probability of a proper amount of paint, but uneven application.