Probability with multiple categories

A question is this type if and only if the population contains three or more distinct categories and probabilities involve combinations across these categories.

3 questions

OCR MEI Paper 2 2021 November Q9
9 Labrador puppies may be black, yellow or chocolate in colour. Some information about a litter of 9 puppies is given in the table.
malefemale
black13
yellow21
chocolate11
Four puppies are chosen at random to train as guide dogs.
  1. Determine the probability that exactly 3 females are chosen.
  2. Determine the probability that at least 3 black puppies are chosen.
  3. Determine the probability that exactly 3 females are chosen given that at least 3 black puppies are chosen.
  4. Explain whether the 2 events ‘choosing exactly 3 females’ and ‘choosing at least 3 black puppies’ are independent events.
Edexcel S1 2002 November Q1
  1. (a) Explain briefly why statistical models are used when attempting to solve real-world problems.
    (b) Write down the name of the distribution you would recommend as a suitable model for each of the following situations.
    1. The weight of marmalade in a jar.
    2. The number on the uppermost face of a fair die after it has been rolled.
      (2)
    3. There are 125 sixth-form students in a college, of whom 60 are studying only arts subjects, 40 only science subjects and the rest a mixture of both.
    Three students are selected at random, without replacement.
    Find the probability that
    (a) all three students are studying only arts subjects,
    (b) exactly one of the three students is studying only science subjects.
OCR Further Statistics 2018 March Q3
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.