OCR Further Statistics 2018 March — Question 3

Exam BoardOCR
ModuleFurther Statistics (Further Statistics)
Year2018
SessionMarch
TopicHypergeometric Distribution
TypeProbability with multiple categories

3 Adila has a pack of 50 cards.
  1. Each of the 50 cards is numbered with a different integer from 1 to 50 . Adila selects 5 cards at random without replacement.
    (a) Find the probability that exactly 3 of the 5 cards have numbers which are 10 or less.
    (b) Adila arranges the 5 cards in a line in a random order. Find the probability that the 5 cards are arranged in numerically increasing order. 10 of the 50 cards are blue and the rest are green.
  2. Adila randomly selects three sets of 10 cards each, without replacement. The sets are labelled \(A , B\) and \(C\). Given that \(A\) contains 3 blue cards and 7 green cards, find the probability that \(B\) contains exactly 2 blue cards and \(C\) contains exactly 3 blue cards.