QCE Vault / Mathematical Methods Mathematical Methods — Question 8 QCAA 2020, Paper 1 · 1 mark
Browse all questions Original practice exam Report an issue Q8 · 2020 · Technology-free Simple familiar 1 mark
QUESTION 8 A test includes six multiple choice questions. Each question has four options for the answer. If the answers are guessed, the probability of getting at most two questions correct is represented by
(A) ( 6 0 ) ( 0.25 ) 0 ( 0.75 ) 6 + ( 6 1 ) ( 0.25 ) 1 ( 0.75 ) 5 \binom60(0.25)^0(0.75)^6+\binom61(0.25)^1(0.75)^5 ( 0 6 ) ( 0.25 ) 0 ( 0.75 ) 6 + ( 1 6 ) ( 0.25 ) 1 ( 0.75 ) 5 (B) ( 6 0 ) ( 0.25 ) 0 ( 0.75 ) 6 + ( 6 1 ) ( 0.25 ) 1 ( 0.75 ) 5 + ( 6 2 ) ( 0.25 ) 2 ( 0.75 ) 4 \binom60(0.25)^0(0.75)^6+\binom61(0.25)^1(0.75)^5+\binom62(0.25)^2(0.75)^4 ( 0 6 ) ( 0.25 ) 0 ( 0.75 ) 6 + ( 1 6 ) ( 0.25 ) 1 ( 0.75 ) 5 + ( 2 6 ) ( 0.25 ) 2 ( 0.75 ) 4 (C) 1 − [ ( 6 0 ) ( 0.25 ) 0 ( 0.75 ) 6 + ( 6 1 ) ( 0.25 ) 1 ( 0.75 ) 5 ] 1-\left[\binom60(0.25)^0(0.75)^6+\binom61(0.25)^1(0.75)^5\right] 1 − [ ( 0 6 ) ( 0.25 ) 0 ( 0.75 ) 6 + ( 1 6 ) ( 0.25 ) 1 ( 0.75 ) 5 ] (D) 1 − [ ( 6 0 ) ( 0.25 ) 0 ( 0.75 ) 6 + ( 6 1 ) ( 0.25 ) 1 ( 0.75 ) 5 + ( 6 2 ) ( 0.25 ) 2 ( 0.75 ) 4 ] 1-\left[\binom60(0.25)^0(0.75)^6+\binom61(0.25)^1(0.75)^5+\binom62(0.25)^2(0.75)^4\right] 1 − [ ( 0 6 ) ( 0.25 ) 0 ( 0.75 ) 6 + ( 1 6 ) ( 0.25 ) 1 ( 0.75 ) 5 + ( 2 6 ) ( 0.25 ) 2 ( 0.75 ) 4 ] WORKED SOLUTION
Answer B 1 mark Worked solution
If X ∼ Bin ( 6 , 0.25 ) X\sim\operatorname{Bin}(6,0.25) X ∼ Bin ( 6 , 0.25 ) , then “at most two” is P ( X = 0 ) + P ( X = 1 ) + P ( X = 2 ) P(X=0)+P(X=1)+P(X=2) P ( X = 0 ) + P ( X = 1 ) + P ( X = 2 ) , which is option B. Worked explanation by QCE Vault; correct option verified against the QCAA answer key.
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