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Properties of Outcomes Practice Problems (page 2)

By — McGraw-Hill Professional
Updated on Oct 25, 2011

Solution

Let the following expressions stand for the respective probabilities, all representing the results of random selections by the coach (and all of which we are told):

  • Probability that a student can swim fast enough = p ( S ) = 200/1000 = 0.200
  • Probability that a student can dive well enough = p ( D ) = 100/1000 = 0.100
  • Probability that a student can play water polo well enough = p ( W ) = 150/1000 = 0.150
  • Probability that a student can swim fast enough and dive well enough = p ( SD ) = 30/1000 = 0.030
  • Probability that a student can swim fast enough and play water polo well enough = p ( SW ) = 110/1000 = 0.110
  • Probability that a student can dive well enough and play water polo well enough = p ( DW ) = 20/1000 = 0.020
  • Probability that a student can swim fast enough, dive well enough, and play water polo well enough = p ( SDW ) = 10/1000 = 0.010

In order to calculate the total number of students who can end up playing at least one sport for this coach, we must find p ( SDW ) using this formula:

p ( SDW ) = p ( S ) + p ( D ) + p ( W )

p ( SD ) – p ( SW ) – p ( DW ) – p ( SDW

= 0.200 + 0.100 + 0.150  – 0.030 – 0.110 – 0.020 – 0.010  

= 0.280

This means that 280 of the students in the school are potential prospects.

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