Stat1

Assignment 1

1. (a) P(W ) = 11=25 = 0:44:

(b) P(B) = 8=25 = 0:32:

(c) P(W \ B) = 4=25 = 0:16:

2. I) The answers depend on a data set and vary from one lab section to another. For example, if we use the following data

Experimental Data for one of the Lab Sections

Sample size = 15

Number of White Balls selected = 8 Number of Blue-dotted Balls selected = 7

Number of White Balls with Blue Dot selected = 3

Number of Blue-dotted Balls selected from the population of White Balls = 4 Number of White Balls selected from the population of Blue-dotted Balls = 8

then

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(a) P(W ) = 8=15 = 0:53:

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(b) P(B) = 7=15 = 0:47:

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(c) P(W \ B) = 3=15 = 0:20:

II) Using the combined results

Combined Experimental Data

Sample size = 196

Number of White Balls selected = 82 Number of Blue-dotted Balls selected = 63

Number of White Balls with Blue Dot selected = 29

Number of Blue-dotted Balls selected from the population of White Balls = 83 Number of White Balls selected from the population of Blue-dotted Balls = 91

we obtain (up to two decimal places)

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P(W ) = 82=196 = 0:42;|P(B) = 63=196 = 0:32;|P(W \ B) = 29=196 = 0:15:|

Comparing the actual and estimated probabilities, we observe that for the combined sample of size n = 196 the relative frequencies estimate the actual probabilities very well, whereas in case of the small sample of size n = 15, the approximation is worse. This is consistent with the definition of probability as the limiting relative frequency. In general, the larger the sample size is, the better the approximation is.

4. (a) The answer depends on a data set and varies from one lab section to another. For

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example, if we use the data above (sample size = 15), then P(BjW ) = 4=15 = 0:27:

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(b) Using the combined results, P(BjW ) = 83=196 = 0:42:

(c) No, the sample spaces used to estimate P(BjW ) and P(B) are...