Refer to the figure accompanying Assignment Problem 31. Consider the case in which two colonies are randomly sampled from the probability distribution shown.

a. Are the events “the first diameter is between 4 and 6” and “the second diameter is between 8 and 12” mutually exclusive? Explain.

b. Are the events “the first diameter is between 4 and 6” and “the second diameter is between 8 and 12” independent? Explain.

c. What is the probability that the first diameter is between 4 and 6 and the second diameter is between 8 and 12?

d. What is the probability that the first diameter is between 8 and 12 or the second diameter is between 10 and 12?

Data from problem 31

 The figure at the bottom of the page shows the probability density of colony diameters (in mm) in a hypothetical population of Paenibacillus bacteria. The distribution is continuous, so the probability of sampling a colony within some range of diameter values is given by area under the curve. Numbers next to the curve indicate the area of the region indicated in red. Consider the case in which a single colony is randomly sampled from the population.

Transcribed Image Text:

0.4 0.3 0.2- Inn 0.1 2 4 6 8 10 12 14 0.4 Probability density 0.3 0.2 0.1 0 0.4 0.3 0.2 0.1 0 0.14 0.48 A 4 6 Colony diameter (mm) -2 8 10 12 14 0- 0.4 0.3 0.2 0.1 0 2 4 6 N. 10 2 0.14 8 10 12 14 0.02 4 6 8 10 12 14 Colony diameter (mm)