Bayes with complementary outcome

Questions specifically asking for P(A|B') where B' is the complement of B (e.g., given NOT late, given does NOT have coffee, given does NOT have jam), requiring calculation of P(B') first.

6 questions · Moderate -0.6

2.03d Calculate conditional probability: from first principles
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CAIE S1 2021 November Q3
5 marks Moderate -0.8
3 For her bedtime drink, Suki has either chocolate, tea or milk with probabilities \(0.45,0.35\) and 0.2 respectively. When she has chocolate, the probability that she has a biscuit is 0.3 When she has tea, the probability that she has a biscuit is 0.6 . When she has milk, she never has a biscuit. Find the probability that Suki has tea given that she does not have a biscuit.
CAIE S1 2016 June Q3
5 marks Moderate -0.8
3 The probability that the school bus is on time on any particular day is 0.6 . If the bus is on time the probability that Sam the driver gets a cup of coffee is 0.9 . If the bus is not on time the probability that Sam gets a cup of coffee is 0.3 .
  1. Find the probability that Sam gets a cup of coffee.
  2. Given that Sam does not get a cup of coffee, find the probability that the bus is not on time.
CAIE S1 2019 June Q2
6 marks Moderate -0.3
2 Megan sends messages to her friends in one of 3 different ways: text, email or social media. For each message, the probability that she uses text is 0.3 and the probability that she uses email is 0.2 . She receives an immediate reply from a text message with probability 0.4 , from an email with probability 0.15 and from social media with probability 0.6 .
  1. Draw a fully labelled tree diagram to represent this information.
  2. Given that Megan does not receive an immediate reply to a message, find the probability that the message was an email.
CAIE S1 2019 March Q1
5 marks Moderate -0.5
1 On each day that Tamar goes to work, he wears either a blue suit with probability 0.6 or a grey suit with probability 0.4 . If he wears a blue suit then the probability that he wears red socks is 0.2 . If he wears a grey suit then the probability that he wears red socks is 0.32 .
  1. Find the probability that Tamar wears red socks on any particular day that he is at work.
  2. Given that Tamar is not wearing red socks at work, find the probability that he is wearing a grey suit.
CAIE S1 2009 November Q3
6 marks Moderate -0.8
3 Maria chooses toast for her breakfast with probability 0.85 . If she does not choose toast then she has a bread roll. If she chooses toast then the probability that she will have jam on it is 0.8 . If she has a bread roll then the probability that she will have jam on it is 0.4 .
  1. Draw a fully labelled tree diagram to show this information.
  2. Given that Maria did not have jam for breakfast, find the probability that she had toast.
CAIE S1 2013 November Q2
5 marks Moderate -0.3
2 On Saturday afternoons Mohit goes shopping with probability 0.25, or goes to the cinema with probability 0.35 or stays at home. If he goes shopping the probability that he spends more than \(\\) 50\( is 0.7 . If he goes to the cinema the probability that he spends more than \)\\( 50\) is 0.8 . If he stays at home he spends \(\\) 10$ on a pizza.
  1. Find the probability that Mohit will go to the cinema and spend less than \(\\) 50\(.
  2. Given that he spends less than \)\\( 50\), find the probability that he went to the cinema.