mcarthyryan
New member
- Joined
- Jan 25, 2017
- Messages
- 21
Probability Question I have got wrong? "5% of the vases, the colour is uneven...."
The question:
A company producing glass vases is experiencing quality issues and has identified the following independent problems.
5% of the vases the colour is uneven.
6% of the vases the glaze is damaged.
4% of the vases have a distorted shape.
What is the overall probability of a vase having one or more of these defects?
Give your answer as a percentage to 1 decimal place.
My answer:
Probability of a vase of having uneven colour, P(C) = 5% = 1/20
Probability of a vase of having a damaged glaze, P(G) = 6% = 3/50
Probability of a vase of having a distorted shape, P(S) = 4% = 1/25
P (≥1 defects)
Probability of having 1 defect: P(1) = P (uneven colour) or P (damaged glaze) or P (distorted shape)
P(1) = 1/20 + 3/50 + 1/25 = 3/20
Probability of having 2 defects: P(2) = P (uneven colour and damaged glaze) or P (uneven colour and distorted shape) or P (damaged glaze and distorted shape)
P(2) = (1/20 x 3/50) + (1/20 x 1/25) + (3/50 x 1/25) = 37/5000
Probability of having 3 defects: P(3) = P (uneven colour, damaged glaze and distorted shape)
P(3) =(1/20 x 3/50 x 1/25) = 3/25000
Therefore P (≥1 defects) = P(1) or P(2) or P(3) = 3/20 + 37/5000 + 3/25000 = 1969/12500 = 0.15752 = 15.8%
So my answer to 1 d.p is 15.8%, but it was marked incorrectly? Please can anyone see where I went wrong?
Thank you
The question:
A company producing glass vases is experiencing quality issues and has identified the following independent problems.
5% of the vases the colour is uneven.
6% of the vases the glaze is damaged.
4% of the vases have a distorted shape.
What is the overall probability of a vase having one or more of these defects?
Give your answer as a percentage to 1 decimal place.
My answer:
Probability of a vase of having uneven colour, P(C) = 5% = 1/20
Probability of a vase of having a damaged glaze, P(G) = 6% = 3/50
Probability of a vase of having a distorted shape, P(S) = 4% = 1/25
P (≥1 defects)
Probability of having 1 defect: P(1) = P (uneven colour) or P (damaged glaze) or P (distorted shape)
P(1) = 1/20 + 3/50 + 1/25 = 3/20
Probability of having 2 defects: P(2) = P (uneven colour and damaged glaze) or P (uneven colour and distorted shape) or P (damaged glaze and distorted shape)
P(2) = (1/20 x 3/50) + (1/20 x 1/25) + (3/50 x 1/25) = 37/5000
Probability of having 3 defects: P(3) = P (uneven colour, damaged glaze and distorted shape)
P(3) =(1/20 x 3/50 x 1/25) = 3/25000
Therefore P (≥1 defects) = P(1) or P(2) or P(3) = 3/20 + 37/5000 + 3/25000 = 1969/12500 = 0.15752 = 15.8%
So my answer to 1 d.p is 15.8%, but it was marked incorrectly? Please can anyone see where I went wrong?
Thank you