QCE Vault / Mathematical Methods Discrete random variables — Question 248 Original QCE Vault practice · 1 mark
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QUESTION 248 Each of five independent mystery envelopes contains a gold card with probability 0.2 0.2 0.2 . The probability that exactly one envelope contains a gold card is (A) 5 ( 0.2 ) ( 0.8 ) 4 5(0.2)(0.8)^4 5 ( 0.2 ) ( 0.8 ) 4 (D) 1 − ( 0.8 ) 5 1-(0.8)^5 1 − ( 0.8 ) 5 WORKED SOLUTION
Answer A 1 mark Worked solution
For X ∼ Bin ( 5 , 0.2 ) X\sim\operatorname{Bin}(5,0.2) X ∼ Bin ( 5 , 0.2 ) , P ( X = 1 ) = ( 5 1 ) ( 0.2 ) ( 0.8 ) 4 P(X=1)=\binom51(0.2)(0.8)^4 P ( X = 1 ) = ( 1 5 ) ( 0.2 ) ( 0.8 ) 4 . Exact answers unless rounding is specified; equivalent forms accepted.
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