# What is the probability that the third fly checked is the first one with white eyes?

What is the probability that the third fly checked is the first one with white eyes?
6. Suppose that the probability is 0.30 that achild who is exposed to chicken pox will catch it.
Also assume that it is reasonable to treat the results for each child as independent.
4-
Suppose that 8 children are exposed to chicken pox. and letX equal the number of
children out of the 8 that actually contract the disease.
a. What kind of distribution does X have? Clearly explain why it satisfies all conditions for
this distribution.
b. What is the probability that ‘2 or fewer of the 8 children contract the disease?
c. On average, if 8 children are exposed to chicken pox. how many would you expect to
contract the disease?
7. In a genetics class. some biology students were asked to check the eye color of a large number
of fruit flies. Based on theoretical considerations from genetics. they expected that 30’: of
the fruit flies would have red eyes and 54’: would have white eyes. They also believe that
the eye colors of different flies are independent of one another.
In each part of the problem, clearly identify which distribution you are using and
briefly explain why you chase that distribution.
a. What is the probability that the third fly checked is the first one with white eyes?
b. What is the probability that the at least one of the first three flies checked will have white
eyes?
c. What is the probability that they will need to check more than 3 flies to find one with white
eyes?
d. What is the probability that exactly 8 of the first 10 flies checked have red eyes?
e. What is the probability that at least 8 of the first 10 flies checked have red eyes?
f. On average. how many flies out of 10 would you expect to have red eyes?
g. What is the probability that the tenth fly checked will be the sixth one with red eyes?
8. A slight modification of the scenario from exercise #6 above: Suppose that the students start
with a group of 40 fruit flies. 30 of which have red eyes and 10 of which have white eyes.
The students then randomly select 10 of the 40 flies. Let Y = the number of flies with red eyes
in the students‘ sample.
a. What kind of distribution does Y have? Why? Make sure that you specify the values of all
parameters.
b. What is the probability that exactly 8 of 10 flies checked have red eyes?
c. What is the probability that at least 8 of 10 flies checked have red eyes?
d. On average. how many flies out of 10 would you expect to have red eyes?
e. How do the answers to (b) through (d) compare with the answers to (d) through (0 in
exercise #6?

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