Question

3. (7 pts) Coach Otis Campbell offered to buy hot dogs for players on his team. Of the 44 players: 6 wanted all three condiments, 11 wanted ketchup(K) and relish(R), 10 wanted ketchup and mustard (M), 8 wanted mustard and relish, 28 wanted ketchup, 20 wanted mustard, and 14 wanted relish a. (3 pts) create a Venn Diagram mato 29 13 4-54 b. How many did not want any of the condiments c. How many wanted at least 2 condiments d. How many wanted at most 2 condiments e. How many wanted 1 condiment

Answer 1

a) Venn diagram

N= Total number of player =44

1v

K : ketchup R: relish M : mustard

n(K) =number of player wanted ketchup = 28

n(M)= number of player wanted mustard =20

n(R) =number of player wanted relish =14

n(K $\cap$ M) =number of player wanted ketchup and mustard = 10

n(K $\cap$ R) =number of player wanted ketchup and relish = 11

n(R $\cap$ M) =number of player wanted relish and mustard = 8

n(K$\cap$ R $\cap$ M) =number of player wanted all the three condiments = 6

from venn diagram

n(K $\cap$ R' $\cap$ M') = number of player exactly want condiment ketup =13

n(K' $\cap$ R $\cap$ M') = number of player exactly want condiment relish =1

n(K' $\cap$ R' $\cap$ M) = number of player exactly want condiment mustard =8

n(K $\cap$ R $\cap$ M') = number of player exactly want condiment ketup and relish =5

n(K $\cap$ R' $\cap$ M) = number of player exactly want condiment ketup and mustard =4

n(K' $\cap$ R $\cap$ M) = number of player exactly want condiment mustard and relish =2

b) number of player did not want any of the condimnets = n( k' $\cap$ M' $\cap$ R')

= n(K U M U R)'

= N - n(KUMUR)

= 44- ( 13 +1 +8 +5 +4 +2 +6)

=44-39

= 5

c) Number of player wanted atleast two condiments

= n(K $\cap$ R $\cap$ M') +n(K $\cap$ R' $\cap$ M) + n(K' $\cap$ R $\cap$ M) + n(K $\cap$ R $\cap$ M)

= 5 +4 +2 +6

= 17

d) Number of player wanted atmost 2 condiments

= n(KUMUR)' +n(K $\cap$ R' $\cap$ M') + n(K' $\cap$ R $\cap$ M') + n(K' $\cap$ R' $\cap$ M) + n(K $\cap$ R $\cap$ M') +n(K $\cap$ R' $\cap$ M) +n(K' $\cap$ R $\cap$ M)

= 5+13+1+8+5+4+2

= 38

e ) Number of player want exactly one condiment

   = n(K $\cap$ R' $\cap$ M') + n(K' $\cap$ R $\cap$ M') + n(K' $\cap$ R' $\cap$ M)

= 13+1+8

= 22