Discrete random variables — Question 125
Original QCE Vault practice · 5 marks
Q125 · Practice questionTechnology-activeComplex unfamiliar5 marks
QUESTION 125 (5 marks)
Let X∼Bin(5,p), where 0<p<1. It is known that P(X=0)=0.32768. Determine p and then calculate P(X≥2). WORKED SOLUTION
Practice marking scheme
5 marksANSWERp=0.20 and P(X≥2)=0.26272. Worked solution
(1−p)5=0.32768=0.85, so p=0.2. Then P(X≥2)=1−P(X=0)−P(X=1)=1−0.32768−5(0.2)(0.8)4=0.26272. Forms the equation for P(X=0). Determines p=0.2. Uses the complement for P(X≥2). Calculates P(X=1) correctly. Obtains 0.26272. Practice question aligned to the current QCAA syllabus; review the worked solution and marking criteria.
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