OCR PURE — Question 11

Exam BoardOCR
ModulePURE
TopicBinomial Distribution
TypeIndependent binomial samples with compound probability

11 The probability that Janice sees a kingfisher on any particular day is 0.3 . She notes the number, \(X\), of days in a week on which she sees a kingfisher.
  1. State one necessary condition for \(X\) to have a binomial distribution. Assume now that \(X\) has a binomial distribution.
  2. Find the probability that, in a week, Janice sees a kingfisher on exactly 2 days. Each week Janice notes the number of days on which she sees a kingfisher.
  3. Find the probability that Janice sees a kingfisher on exactly 2 days in a week during at least 4 of 6 randomly chosen weeks.