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

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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) About Me  (Show Source):
You can put this solution on YOUR website!
There are
9%2A8%2A7%2A6%2F%281%2A2%2A3%2A4%29=126 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 8%2A7%2A6%2F%281%2A2%2A3%29=56
Of the total of 126 possible groups of 4 mice,
there are 56 such groups including Mike Mouse.
The probability that Mike mouse will be included is
56%2F126=highlight%284%2F9=%220.4444...%22=%2244%25%28rounded%29%22%29

A different way:
As you select the first mouse,
the probability of not selecting Mike Mouse is 8%2F9 .
After that, the probability of not picking Mike as your second Mouse is 7%2F8 .
After that, the probability of not picking Mike as your third Mouse is 6%2F7 .
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 5%2F6 .
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
1-5%2F9=highlight%284%2F9%29 .