Question 916971: I am studying 55 children and 3 movies, The Lion King, Shrek and Finding Nemo
17 saw the lion king, 17 saw shrek, 23 saw Nemo, 6 saw King & Shrek
8 saw king & nemo, 10 saw shrek & nemo, 2 saw all 3 movies.
what is the probability a child saw:
1) exactly 2 of them
2) exactly 1 of them
3) None of them
4) only the lion king
5) at least shrek & nemo
please help I don't know what to do first!!!!
I havn't been in math class in over 20 years.
thank you
Found 2 solutions by Theo, ewatrrr:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the basic assumption in these types of problems is that all the numbers are inclusive.
what this means is:
the ones that saw lion king includes the ones that saw:
lion king and shrek
lion king and nemo
lion king and shrek and nemo.
the ones that saw shrek includes the ones that saw:
lion king and shrek
shrek and nemo
lion king and shrek and nemo.
the ones that saw nemo includes the ones that saw:
lion king and nemo
shrek and nemo
lion king and shrek and nemo.
the ones that saw lion king and shrek includes the ones that saw:
lion king and shrek and nemo.
the ones that saw lion king and nemo includes the ones that saw:
lion king and shrek and nemo.
the ones that saw shrek and nemo includes the ones that saw:
lion king and shrek and nemo.
you need to split out the inclusives to get the onlys.
what you want to get is:
the ones that saw lion king only.
the ones that saw shrek only.
the ones that saw nemo only.
the ones that saw lion king and shrek only.
the ones that saw lion king and nemo only.
the ones that saw shrek and nemo only.
the ones that saw all 3 lion king and shrek and nemo only.
work your way from the bottom up is the easiest way to do this.
this would be the least inclusive to the most inclusive.
the least inclusive is the ones that saw all 3.
the next lest inclusive is the ones that saw 2 of the 3.
the most inclusive is the ones that saw 1 out of the 3.
start with the ones that saw all 3.
that number is 2.
there is nothing else included in that number so there's nothing to subtract.
the ones that saw all 3 DISABLED_event_only= 2 *****
next go with the pairs.
the ones that saw lion king and shrek = 6
subtract 2 that saw all 3.
the ones that saw lion king and shrek DISABLED_event_only= 6 - 2 = 4 *****
the ones that saw lion king and nemo = 8
subtract 2 that saw all 3.
the ones that saw lion king and nemo DISABLED_event_only= 8 - 2 = 6 *****
the ones that saw shrek and nemo = 10
subtract 2 that saw all 3.
the ones that saw shrek and nemo DISABLED_event_only= 10 - 2 = 8 *****
next go with the singles.
the ones that saw lion king = 17
subtract 2 that saw all 3.
subtract 4 that saw lion king and shrek only.
subtract 6 that saw lion king and nemo only.
the ones that saw lion king DISABLED_event_only= 17 - 3 - 4 - 6 = 5 *****
the ones that saw shrek = 17
subtract 2 that saw all 3.
subtract 4 that saw lion king and shrek only.
subtract 8 that saw shrek and nemo only.
the ones that saw shrek DISABLED_event_only= 17 - 2 - 4 - 8 = 3 *****
the ones that saw nemo = 23
subtract 2 that saw all 3.
subtract 8 that saw shrek and nemo only.
subtract 6 that saw lion king and nemo only.
the ones that saw nemo DISABLED_event_only= 23 - 2 - 8 - 6 = 7 *****
you now have made all the categories non inclusive as follows:
the ones that saw all 3 = 2
the ones that saw lion king and shrek DISABLED_event_only= 4
the ones that saw lion king and nemo DISABLED_event_only= 6
the ones that saw shrek and nemo DISABLED_event_only= 8
the ones that saw lion king DISABLED_event_only= 5
the ones that saw shrek DISABLED_event_only= 3
the ones that saw nemo DISABLED_event_only= 7
add them up and you get a total of 2 + 4 + 6 + 8 + 5 + 3 + 7 = 35
now that you have the data, you can answer the questions.
the questions are:
what is the probability a child saw:
1) exactly 2 of them
2) exactly 1 of them
3) None of them
4) only the lion king
5) at least shrek & nemo
use your final data list to answer these questions.
the data list is shown here again for your ease of reference and to clearly identify what i meant.
final data list:
the ones that saw all 3 = 2
the ones that saw lion king and shrek DISABLED_event_only= 4
the ones that saw lion king and nemo DISABLED_event_only= 6
the ones that saw shrek and nemo DISABLED_event_only= 8
the ones that saw lion king DISABLED_event_only= 5
the ones that saw shrek DISABLED_event_only= 3
the ones that saw nemo DISABLED_event_only= 7
total who saw 1 or 2 or 3 movies is 35 out of 55.
that makes 20 that didn't see any movies at all.
answer to question 1:
number of children that saw exactly 2 movies = 4 + 6 + 8 = 18.
probability is 18/55.
these are the ones that saw:
lion king and shrek only.
lion king and nemo only.
shrek and nemo only.
answer to question 2:
number of children that saw exactly 1 movie = 5 + 3 + 7 = 15
probability is 15/55.
these are the ones that saw:
lion king only.
shrek only.
nemo only.
answer to question 3:
none of them.
there are 35 children who saw 1 or 2 or 3 movies out of 55 children in total.
that leaves 20 that didn't see any movies at all.
probability is 20/55.
answer to question 4:
number of children that saw lion king DISABLED_event_only= 5
probability is 5/55
answer to question 5:
number of children who saw at least shrek and nemo would include:
number who saw shrek and nemo only.
number who saw all 3 of lion king and shrek and nemo.
that number is equal to 8 + 2 = 10
probability is 10/55
these problems can be confusing, but if you work them in a systematic manner, you should do ok. with all the numbers floating around, they're still confusing but you have a better chance of solving them if you do them in a systematic manner.
work from the least inclusive to the the most inclusive.
the ones who saw all 3 are the least inclusive.
the ones who saw two out of the 3 are the next least inclusive because they only include the ones that saw all 3.
the ones who saw 1 out of the 3 are the most inclusive because they include the ones who saw two out of three plus the ones that saw all three.
you can also check your work by using the formula that takes care of situations like this.
that formula is:
p(k or s or n) = p(k) + p(s) + p(n) - p(ks) - p(kn) - p(sn) + p(ksn)
in this formula, the inclusives are used.
k = 17
s = 17
n = 23
ks = 6
kn = 8
sn = 10
ksn = 2
t = 55
p(k) = k/t = 17/55
p(s) = s/t = 17/55
p(n) = n/t = 23/55
p(ks) = ks/t = 6/55
p(kn) = kn/t = 8/55
p(sn) = sn/t = 10/55
p(ksn) = ksn/t = 2/55
formula becomes:
p(k or s or n) = p(k) + p(s) + p(n) - p(ks) - p(kn) - p(sn) + p(ksn) becomes:
p(k or s or n) = 17/55 + 17/55 + 23/55 - 6/55 - 8/55 - 10/55 + 2/55 which becomes:
p(k or s or n) = 35/55.
the number of 35 agrees with the total number of students that saw 1 only or 2 only or 3 only movies so that confirms that you categorized correctly.
Answer by ewatrrr(24785)  (Show Source):
You can put this solution on YOUR website! Sketch Circles: Fill Diagram from the INside ..out
P(exactly 2 of them)= 18/55
P(exactly 1 of them) = 15/55 = 3/11
P(None of them) = 20/55 = 4/11
P(only the lion king) 5/55 = 1/11
P(at least shrek & nemo = (5+3+2)/55 = 10/55 = 2/11
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