On a 5 question multiple-choice test, where each question has 4 answers, what would be the probability of getting at least 1 question wrong?

Assuming that each answer was chosen by random selection, the probability of getting all right would be (1/4)^5. The probability of getting at least one wrong would be 1-(1/4)^5 = 1023/1024 = 0.999 = 99.9%

Ans: 1-(1/4)^5 = 0.999 = 99.9%

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p = probability of a success ( one correct answer out of four given choices )

q = probability of a failure ( three wrong answers out of four given choices )

p = ¼

q = ¾

P( getting all five questions correct ) = p⁵

P( getting all five questions correct ) = ( ¼ )⁵

P( getting all five questions correct ) = 1/1024

P( getting at least 1 question wrong ) = 1 - P( getting all five questions correct )

P( getting at least 1 question wrong ) = 1 - 1/1024

P( getting at least 1 question wrong ) = 1023/1024

1 - (probability of getting all 5 correct) = ?