SOLUTION: A multiple-choice test consists of 7 questions. Each question has answer choices of a ,b ,c , and d , and only one of the choices is correct. If a student randomly guesses on eac

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Question 1098972: A multiple-choice test consists of 7 questions. Each question has answer choices of a ,b ,c , and d , and only one of the choices is correct. If a student randomly guesses on each question, what is the probability that she gets at most 1 of them correct?
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
That's a binomial probability problem with n=7 trials, p = 1/4,
and x=0 OR x=1

There are two ways, by formula or by graphing calculator.

By formula first (the long way):

expr%28n%21%2F%28x%21%28n-x%29%21%29%29p%5Ex%2A%281-p%29%5E%28n-x%29

Using x=0

expr%287%21%2F%280%21%287-0%29%21%29%29%281%2F4%29%5E0%2A%281-1%2F4%29%5E%287-0%29

expr%287%21%2F%281%287%29%21%29%29%281%29%2A%283%2F4%29%5E7

expr%287%21%2F%287%21%29%29%281%29%2A%283%5E7%2F4%5E7%29

%281%29%281%29%282187%2F16384%29

2187%2F16384

Using x=1

expr%287%21%2F%281%21%287-1%29%21%29%29%281%2F4%29%5E1%2A%281-1%2F4%29%5E%287-1%29

expr%287%21%2F%281%286%29%21%29%29%281%2F4%29%2A%283%2F4%29%5E6

expr%287%21%2F%286%21%29%29%281%2F4%29%2A%283%5E6%2F4%5E6%29





7%2A%28729%2F16384%29

5103%2F16384

Use the fact that OR means to ADD

2187%2F16384%22%22%2B%22%225103%2F16384

7290%2F16384

0.4449462891

By graphing calculator, if you have a TI-83 or TI-84,

Press 2ND VARS
Scroll to binomcdf(
Press ENTER

You may or may not see the next screen, depending of
the age of your calculator or the settings in MODE
If you see this screen, make it read this way:

                binomcdf
         trials:7
         p:1/4
         x value:1
         Paste

If you have that screen, scroll to 'Paste' and press ENTER

Whether you have that screen or not you should have this on
your main screen, whether you have to type it in or it's
already there:

binomcdf(7,1/4,1)

Press ENTER

Read    .4449462884

Edwin