Answer questions 4-6 fully and show work. The settlement of a bridge pier, say P

Question

Answer questions 4-6 fully and show work.

The settlement of a bridge pier, say Pier 1, is estimated to be between 2 and 5 cm. Similarly, the settlement of an adjacent pier, Pier 2, is also estimated to be between 4 and 10 cm. There will, therefore, be a possibility of differential settlements between these two adjacent piers. a. What would be the sample space of this differential settlement? b. If the differential settlements in the above sample space are equally likely, what would be the probability that the differential settlement will be between 3 and 5 cm? 10 soil samples have been collected by a researcher. 5 out of the 10 are dissolved inorganic matter samples: 3 of them are dissolved organic matter samples: the other 2 are heavy metal samples. a. A researcher decided to choose 3 samples randomly. What is the probability that all of the 3 samples are dissolved inorganic carbon samples? b. A researcher decided to choose 3 samples randomly. What are the possible outcomes and how many combinations are there for each of the outcome? Lead and arsenic can contaminate drinking water systems in a city. The probability of lead and arsenic contamination is 0.2 and 0.1, respectively. Assume that contaminations by lead and by arsenic are statistically independent. a. What is the probability that the drinking water system in any given city is contaminated? b. Six cities are currently at the risks of drinking water contamination. Four of the cities are exposed to lead contamination: and the other 2 are exposed to arsenic contamination. A group of undergrad students wanted to investigate the water contamination situation at 2 of the 6 cities. What is the probability that the two cities that they chose are both at risk of lead contamination?

Explanation / Answer

(5)

P(all 3 samples are dissolved inorganic samples) = 5C3/10C3 = 0.0833

Possible outcomes are:

(i)

All 3 are inorganic

Number of combinations = 5C3

(ii)

2 inorganic, 1 organic

Number of combinations = 5C2*3C1

(iii)

2 inorganic, 1 heavy metal

Number of combinations = 5C2*2C1

(iv)

1 inorganic, 2 heavy metals

Number of combinations = 5C1*2C2

(v)

1 inorganic, 2 organic

Number of combinations = 5C1*3C2

(vi)

1 inorganic, 1 organic, 1 heavy metal

Number of combinations = 5C1*3C1*2C1

(vii)

2 organic, 1 heavy metal

Number of combinations = 3C2*2C1

(viii)

1 organic, 2 heavy metals

Number of combinations = 3C1*2C2

So there are total 8 possible outcomes, each with the above mentioned combinations.

Hope this helps !

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