At least one success in repeated trials

A question is this type if and only if it asks for the probability of at least one occurrence of an event across multiple independent or dependent trials.

2 questions · Standard +0.6

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Edexcel S1 Q2
8 marks Standard +0.3
A darts player throws two darts, attempting to score a bull's-eye with each. The probability that he will achieve this with his first dart is \(0.25\). If he misses with his first dart, the probability that he will also miss with his second dart is \(0.7\). The probability that he will miss with at least one dart is \(0.9\).
  1. Show that the probability that he succeeds with his first dart but misses with his second is \(0.15\). [5 marks]
  2. Find the conditional probability that he misses with both darts, given that he misses with at least one. [3 marks]
SPS SPS SM Statistics 2024 January Q5
7 marks Standard +0.8
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 at least 3 black puppies are chosen. [3]
  2. Determine the probability that exactly 3 females are chosen given that at least 3 black puppies are chosen. [3]
  3. Explain whether the 2 events 'choosing exactly 3 females' and 'choosing at least 3 black puppies' are independent events. [1]