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A marketing agency has developed three vacation packages to promote a timeshare plan at a new resort. They estimate that 10​% of potential customers will choose the Day​ Plan, which does not include overnight​ accommodations; 10​% will choose the Overnight​ Plan, which includes one night at the​ resort; and 80​% will choose the Weekend​ Plan, which includes two nights. Complete parts a and b below.

The first step to answering this question is to draw the probability table. 

x p x.p
0 0.1 0
1 0.1 0.1
2 0.8 1.6
     
sum   1.7
     

 Therefore, 1.7 is the expected number of nights. 

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