OCR FS1 AS 2018 March — Question 3

Exam BoardOCR
ModuleFS1 AS (Further Statistics 1 AS)
Year2018
SessionMarch
TopicHypergeometric Distribution
TypeConditional probability in hypergeometric context

3 A pack of 40 cards consists of 10 cards in each of four colours: red, yellow, blue and green. The pack is dealt at random into four "hands", each of 10 cards. The hands are labelled North, South, East and West.
  1. Find the probability that West has exactly 3 red cards.
  2. Find the probability that West has exactly 3 red cards, given that East and West have between them a total of exactly 5 red cards.
  3. South has 5 red cards and 5 blue cards. These cards are placed in a row in a random order. Find the probability that the colour of each card is different from the colour of the preceding card.