OCR S4 2012 June — Question 1

Exam BoardOCR
ModuleS4 (Statistics 4)
Year2012
SessionJune
TopicIndependent Events
TypeCalculate probabilities using independence
1 Independent random variables \(X\) and \(Y\) have distributions \(\mathrm { B } ( 7 , p )\) and \(\mathrm { B } ( 8 , p )\) respectively.
  1. Explain why \(X + Y \sim \mathrm {~B} ( 15 , p )\).
  2. Find \(\mathrm { P } ( X = 2 \mid X + Y = 5 )\).
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