Question 10 In the ACT test, there are 60 multiple choice questions, each with s

Question

Question 10 In the ACT test, there are 60 multiple choice questions, each with six possible answers (A, B, C, D, E, F, one of which is correct. Suppose you guess the answers to the first four questions. (9 point a) Find the probability that the first three guesses are wrong and the fourth is correct, P(wwwc) where C represents a correct answer and W represents a wrong answer. Show work! Make a complete list of the different possible arrangements of three wrong answers and one correct answer. b) c) Find the probability of getting exactly one correct answer when four guesses are made. Show work?

Explanation / Answer

Solution :

n = 4

p =1 / 6 = 0.1666

q = 5 / 6 = 0.8333

( a )

the probability that first three guesses are wrong and fourth is correct = ( 5 / 6 ) * ( 5 / 6 ) * ( 5 / 6 ) * ( 1 / 6 )

= 0.0964

( b )

list of different possible arrangements of three wrongs and one correct answer

= ( C W W W ) , ( W C W W ) , ( W W C W ) , ( W W W C )

( c )

Formula ;

P( k out of n) = n!*pk * qn-k / k! *(n - k)!

the probability of getting one correct answer in four guesses = P( x = 1 )

= 4!*0.16661 * 0.83334-3 / 1! *(4 - 1)!

= 0.3858

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