# SOLUTION: Eloise has put 5 cans (all of the same size) on her kitchen counter; 2 cans of vegetables, 2 cans of soup, and 1 can of peaches. Her son Andy, takes the labels off the cans and th

Algebra ->  Algebra  -> Probability-and-statistics -> SOLUTION: Eloise has put 5 cans (all of the same size) on her kitchen counter; 2 cans of vegetables, 2 cans of soup, and 1 can of peaches. Her son Andy, takes the labels off the cans and th      Log On

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 Click here to see ALL problems on Probability-and-statistics Question 116156: Eloise has put 5 cans (all of the same size) on her kitchen counter; 2 cans of vegetables, 2 cans of soup, and 1 can of peaches. Her son Andy, takes the labels off the cans and throws them away. Eloise then chooses 2 cans at random to open. Find the probability that she will open at least 1 can of soup. Answer by Edwin McCravy(8909)   (Show Source): You can put this solution on YOUR website!Eloise has put 5 cans (all of the same size) on her kitchen counter; 2 cans of vegetables, 2 cans of soup, and 1 can of peaches. Her son Andy, takes the labels off the cans and throws them away. Eloise then chooses 2 cans at random to open. Find the probability that she will open at least 1 can of soup. ``` Whenever you see the words "at least one" always think of this principle: P(at least one) = 1 - P(none at all) So therefore P(she will open at least 1 can of soup) = 1 - P(she will open no cans of soup) = 1 - P(she will open 2 of the 3 non-soup cans) = no. of ways to choose 2 of the 3 non-soup cans 1 - -------------------------------------------------- no. of ways to choose any 2 of the 5 cans C(3,2) 3 7 1 - ------- = 1 - ---- = ---- = 0.7 C(5,2) 10 10 It's not too hard to check this: Suppose the 2 cans of vegetables are called V1 and V2 Suppose the 2 cans of soup are called S1 and S2 Suppose the 1 can of peaches is called P. So she can choose any of these ten pairs of cans: 1. {V1,V2} 2. {V1,S1} at least one soup can 3. {V1,S2} at least one soup can 4. {V1,P} 5. {V2,S1} at least one soup can 6. {V2,S2} at least one soup can 7. {V2,P} 8. {S1,S2} at least one soup can 9. {S1,P} at least one soup can 10. {S2,P} at least one soup can She will have at least one can of soup if she chooses 2, 3, 5, 6, 7, 9, or 10. That's 7 out of 10, or a probability of 7/10. Edwin```