SOLUTION: A survey of 60 people found 40 people liked lemonade and 30 liked cola. Two people said they disliked both. If one person is chosen at random what is the probability that this pers

Algebra ->  Probability-and-statistics -> SOLUTION: A survey of 60 people found 40 people liked lemonade and 30 liked cola. Two people said they disliked both. If one person is chosen at random what is the probability that this pers      Log On


   



Question 1089999: A survey of 60 people found 40 people liked lemonade and 30 liked cola. Two people said they disliked both. If one person is chosen at random what is the probability that this person;
a)likes lemonade
b)likes lemonade only
c)likes cola
d)likes both lemonade and cola
e)does not like lemonade
f)likes lemonade or cola

Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
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A survey of 60 people found 40 people liked lemonade and 30 liked cola. Two people said they disliked both.
If one person is chosen at random what is the probability that this person;
a) likes lemonade
b) likes lemonade only
c) likes cola
d) likes both lemonade and cola
e) does not like lemonade
f) likes lemonade or cola
~~~~~~~~~~~~~~~~~~~~

From the condition, 40 people like lemonade, 30 like cola, and 60-2 = 58 like lemonade or cola.

It implies that  (40+30) - 58 = 12 like both lemonade and soda.

    // See the lesson referred at the end of my post to get understanding why it is so.  


Then  40-12 = 28  like lemonade only,  and  30-12 = 18 like cola only.

Now you can answer all questions:

If one person is chosen at random what is the probability that this person

a) likes lemonade                    40%2F60 = 2%2F3.

b) likes lemonade only               28%2F60 = 7%2F15.

c) likes cola                        30%2F60 = 1%2F2.

d) likes both lemonade and cola      12%2F60 = 1%2F5.

e) does not like lemonade            %2860-40%29%2F60 = 20%2F60 = 1%2F3.

f) likes lemonade or cola            58%2F60 = 29%2F30.

All questions are answered.

For details and better understanding see the lesson
    - Counting elements in sub-sets of a given finite set
in this site.