SOLUTION: in a class that consists of 50, 35 use facebook,25 use instagram. a) what is the max/min number that use both. b) suppose 20 students use both, if a student randomly sele

Question 987530: in a class that consists of 50, 35 use facebook,25 use instagram. a) what is the max/min number that use both. b) suppose 20 students use both, if a student randomly selected, what is the probability that the student doesn't use either facebook or instagram?
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
a)

35+25 = 60 which is 10 over 50

so 10 could use both (35-10 = 25 use facebook only, 25-10 = 15 use instagram only). This is the min number that is in the "both" portion. The max would be the number 25 since it's the smaller of the two (25 and 35). If 25 people use both, then all of the instagram users would also be facebook users, but not the other way around.

In summary:
min number that use both = 10
max number that use both = 25

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b)

"suppose 20 students use both" so we know that 35-20 = 15 use facebook only and 25-20 = 5 use instagram only. In total, we have 15+5+20 = 40 users who use either service or both.

There are 50 people in the class, making 50-40 = 10 people who use neither service.

P(use neither service) = (# of people who use neither service)/(# total)
P(use neither service) = 10/50
P(use neither service) = 1/5
P(use neither service) = 0.2

Answer as a fraction: 1/5
Answer as a decimal: 0.2
Answer as a percentage: 20%

The three answer formats all represent the same probability

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
in a class that consists of 50, 35 use facebook,25 use instagram. a) what is the max/min number that use both. a) what is the max/min number that use both.
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Draw two intersecting circles inside a rectangle.
Label the circles F and I
F = 35 ; I = 25
Put "x" in the intersection.
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a) what is the max/min number that use both.
F has two sections: x and 35-x
I has two sectiions: x and 25-x
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Equation:
35-x + x + 25-x <= 50
60-x <= 50
x >= 10
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b) suppose 20 students use both, if a student randomly selected, what is the probability that the student doesn't use either facebook or instagram?
20 in the intersection
At most 30 are in the rectangle and not in F or I
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Cheers,
Stan H.
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