NAME____________

1. Cds fvde wgryt? A) qrs B) pwr C)xzy 2. Stre hyvf whjut? A) qrs B) pwr C)xzy 3. Hytre de wgryt? A) qrs B) pwr C)xzy 4. Jgrtevde wgryt? A) qrs B) pwr C)xzy 5. Chjoiide wgryt? A) qrs B) pwr C)xzy 6. Ads fvde wgryt? A) qrs B) pwr C)xzy 7. Clwiry tun gryt? A) qrs B) pwr C)xzy 8. Sqrtevde wgryt? A) qrs B) pwr C)xzy 9. Ods fvde wgryt? A) qrs B) pwr C)xzy10. Xzzyiuhkkgryt? A) qrs B) pwr C)xzy

A multiple choice test

has 10 questions …..

There are 3 choices

for each answer.

If you guess everyanswer, what is theprobability that youget 100% correct?

A B C 1 2 3 4 5 6 7 8 910

A B C 1 2 3 4 5 6 7 8 910

A B C 1 2 3 4 5 6 7 8 910

A B C 1 2 3 4 5 6 7 8 910

A B C 1 2 3 4 5 6 7 8 910

Here are a few of the many possible ways of answering this test:

XXX

XXX

XX

XX

X X X XXXXX

X X X XX

XX

XX

XX

XX

XXX

X

X

X

XX

XX

XX

X

XX

XX

X

X

Use the sequential counting principle to count all possibleways of answering the test:

Step 1:answerquestion1

Step 2:answerquestion2

Step 3:answerquestion3

Step 10:answerquestion10………………...

3 x 3 x 3 x ……………… x 3 10

= 3 = 59,049 possible ways to fill in the answer sheet

Of the 59,049 possibilities, only 1 is a perfect paper.

The probability of guessing everything right is 1/59049 !

NAME____________

1. Cds fvde wgryt? A) qrs B) pwr C)xzy 2. Stre hyvf whjut? A) qrs B) pwr C)xzy 3. Hytre de wgryt? A) qrs B) pwr C)xzy 4. Jgrtevde wgryt? A) qrs B) pwr C)xzy 5. Chjoiide wgryt? A) qrs B) pwr C)xzy 6. Ads fvde wgryt? A) qrs B) pwr C)xzy 7. Clwiry tun gryt? A) qrs B) pwr C)xzy 8. Sqrtevde wgryt? A) qrs B) pwr C)xzy 9. Ods fvde wgryt? A) qrs B) pwr C)xzy10. Xzzyiuhkkgryt? A) qrs B) pwr C)xzy

Now consider the

probability that you

guess 7 right and

3 wrong.

First, measure the probability that the first 7 answers are right and thefinal 3 answers are wrong:

# ways to answerthe first 7correctly:

1

# ways to answerquestion 8incorrectly:

x 2

# ways to answerquestion 9incorrectly:

x 2

# ways to answerquestion 10incorrectly:

x 2

The probability that the first 7 answers are right and thefinal 3 answers are wrong = 8/59049

The number of ways of choosing a combination of

7 of the 10 questions to answer correctly =

10 C 7 = 10 x 9 x 8 x 7 x 6 x 5 x 4 = 120 7 x 6 x 5 x 4 x 3 x 2 x 1

The probability that the first 7 answers are right and thefinal 3 answers are wrong = 8/59049

The probability of answering 70% of the test correctly =

(120) x (8/59049) = 960/59049 = .016...