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Probability, STD2 S2 2016 HSC 28c

A cricket team is about to play two matches. The probability of the team having a win, a loss or a draw is 0.7, 0.1 and 0.2 respectively in each match. The possible results in the two matches are displayed in the probability tree diagram.
  

2ug-2016-hsc-q28_2

  1. What is the probability of the team having a win and a draw, in any order?   (2 marks)

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  2. Paul claims that 1.4 is the probability of the team winning both matches.

     

    Give one reason why this is NOT correct.   (1 mark)

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Show Answers Only

i.    `0.28`

ii.   `text(Probabilities cannot exceed 1.)`

Show Worked Solution

i.    `P(W\ text(and)\ D)`

`= P(W,D) + P(D,W)`

`= 0.7 xx 0.2 + 0.2 xx 0.7= 0.28`

♦ Mean mark (i) 45%.
♦ Mean mark (ii) 49%.

 
ii.
   `text(Probabilities cannot exceed 1.)`

Filed Under: Multi-stage Events, Multi-Stage Events, Single and Multi-Stage Events, Single and Multi-Stage Events, Single and Multi-Stage Events Tagged With: Band 5, num-title-ct-corea, smc-1135-10-Probability Trees, smc-4238-10-Dependent events, smc-4238-50-Probability trees, smc-6887-30-Probability Trees, smc-6935-10-Probability Trees, smc-829-10-Probability Trees

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