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80
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Forty-five percent of Americans like to cook and 59% of Americans like to shop, while 23% enjoy both activities. What is the probability that a randomly selected American either enjoys cooking or shopping or both

 Mar 18, 2020
 #1
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Forty-five percent of Americans like to cook and 59% of Americans like to shop, while 23% enjoy both activities. What is the probability that a randomly selected American either enjoys cooking or shopping or both 

 

The question can not mean that 45% like only to cook, and 59% like only to shop, each exclusive of the other... the groups must overlap because the total is more than 100%.  That means we can disregard the 23% because each of those is already accounted for within the other two groups. So that leaves the problem of the 45% cookers and the 59% shoppers.  Since we don't know the extent of their overlap, I think there isn't enough information to solve the problem under the conditions.  I hope I'm wrong and somebody else can solve it.  I'll be interested to learn how. 

 Mar 18, 2020
 #2
avatar+29984 
+2

"Forty-five percent of Americans like to cook and 59% of Americans like to shop, while 23% enjoy both activities. What is the probability that a randomly selected American either enjoys cooking or shopping or both"

 

22% only like to cook,  36% only like to shop,  23% like to do both  (22+23 = 45; 36+23 = 59), so 19% don't like either. Hence probability of choosing one who likes one or the other or both is 1-0.19 or 0.81

 Mar 18, 2020
 #3
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So basically what you did was add 0.45 and 0.59 then subtract 0.23 to obtain 0.81?  Is that it? 

Guest Mar 18, 2020
 #4
avatar+23553 
+1

Here is a Venn diagram:

 Mar 18, 2020

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