a student takes a true false test consisting of 15 questions. assuming that the student guesses at each question, find the probability that the student answers exactly 13 question correctly.

Question

anonymous · Answer

please help

anonymous · Answer

the instructions said to use counting rules to determine the probability

anonymous · Answer

13 ways?

anonymous · Answer

how can you solve that? i still dont understand

anonymous · Answer

could you help me find the answer?

campbell_st · Answer

ok... so here is an alternate method 

Question     choices     P (correct answer)
 
1                     2                 1/2

2                     2                 1/2 x 1/2 = 1/4

3                     2                 1/2 x 1/2 x 1/2 = 1/8

4                   2                   1/2 x 1/2 x 1/2 x 1/2 = 1/16

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the pattern continues.....   for 13 correct.... 

in general its (1/2)^n     n is the number of correct answers

anonymous · Answer

could you please give me the answer? i am not a s good at this as you, even if i try

campbell_st · Answer

just calculate 

$$P(13~~correct) =(\frac{1}{2})^{13}$$

zarkon · Answer

$${15\choose 13}\left(\frac{1}{2}\right)^{15}$$

zarkon · Answer

13 right...then they must have 2 wrong