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Questions › DSE › DSE 2015 › Q52
2 marks, −0.666666666666667Statistics › Random variables and standard distributions › The binomial distributionHardabout 4 min

DSE 2015 Question 52: Random variables and standard distributions

From the square with vertices (0,0),(0,2),(2,0),(2,2)(0,0),(0,2),(2,0),(2,2)(0,0),(0,2),(2,0),(2,2), five points are chosen independently at random. If a point (x,y)(x,y)(x,y) satisfies x+2y≤2x+2y\le2x+2y≤2 a pair of dice is rolled, otherwise a single die; NNN is the total number of dice rolled. For 5≤n≤105\le n\le105≤n≤10, P(N=n)P(N=n)P(N=n) equals

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From the square with vertices (0,0),(0,2),(2,0),(2,2), five points are chosen independently at random. If a point (x,y) satisfies x+2y≤2 a pair of dice is rolled, otherwise a single die; N is the total number of dice rolled. For 5≤ n≤10, P(N=n) equals (A) C(5, n-5)(1/2)ⁿ⁻⁵(1/2)⁵⁻⁽ⁿ⁻⁵⁾ (B) C(10, n-10)(1/4)ⁿ⁻¹⁰(3/4)ⁿ (C) C(5, n-5)(1/4)ⁿ⁻⁵(3/4)¹⁰⁻ⁿ (D) C(10, n-10)(1/2)ⁿ⁻¹⁰(1/2)ⁿ

Also written as: From the square with vertices (0,0),(0,2),(2,0),(2,2), five points are chosen independently at random. If a point (x,y) satisfies x+2y<=2 a pair of dice is rolled, otherwise a single die; N is the total number of dice rolled. For 5<= n<=10, P(N=n) equals

Random variables and standard distributions has come up 173 times in 7 exams since 2005.

What this question tests

This question is on The binomial distribution, part of Random variables and standard distributions in Statistics.

The number of successes in a fixed number of independent trials.

TestStop has 21 past-paper questions on this subtopic.

Practise Random variables and standard distributionsMore on The binomial distribution

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Question from the DSE 2015 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.