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.

2 questions · Standard +0.8

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OCR MEI Paper 2 2021 November Q9
10 marks Standard +0.8
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.
OCR Further Statistics 2018 March Q3
9 marks Standard +0.8
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.
    1. Find the probability that exactly 3 of the 5 cards have numbers which are 10 or less.
    2. 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.
    3. 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.