SOLUTION: Suppose 9 mice are available for a study of a possible carcinogen and 4 of themwill form a control group (i.e. will not receive the substance). Assuming that a random sample of 4 m

Question 923983: Suppose 9 mice are available for a study of a possible carcinogen and 4 of themwill form a control group (i.e. will not receive the substance). Assuming that a random sample of 4 mice are selected, what is the probability that a particular mouse, Mike Mouse will be included in the control group?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
There are
possible groups of 4 mice.
Some of those include Mike Mouse.
How many groups of 4 mice including Mike Mouse are there?
As many as groups of 3 mice made from the other eight mice.
That is
Of the total of possible groups of 4 mice,
there are such groups including Mike Mouse.
The probability that Mike mouse will be included is

A different way:
As you select the first mouse,
the probability of not selecting Mike Mouse is .
After that, the probability of not picking Mike as your second Mouse is .
After that, the probability of not picking Mike as your third Mouse is .
And, if you have not picked Mike Mouse as one of the first 3 mice you pick,
the probability of not picking Mike as your fourth Mouse is .
All in all, the probability of not picking Mike Mouse as one of you four control mice is
.
So the probability of that not happening, and having Mike in your control group is
.
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