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# Properties of Outcomes Practice Problems (page 2)

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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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