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Probability, MET1 2008 VCAA 7

Jane drives to work each morning and passes through three intersections with traffic lights. The number `X` of traffic lights that are red when Jane is driving to work is a random variable with probability distribution given by
 

met1-2008-vcaa-q7
 

  1. What is the mode of `X`?  (1 mark)
  2. Jane drives to work on two consecutive days. What is the probability that the number of traffic lights that are red is the same on both days?  (2 marks)
Show Answers Only
  1. `3`
  2. `0.3`
Show Worked Solution

a.   `3`
 

b.   `text(Pr)(0,0) + text(Pr)(1,1) + text(Pr)(2,2) + text(Pr)(3,3)`

`= 0.1^2 + 0.2^2 + 0.3^2 + 0.4^2`

`= 0.3`