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The Venn diagram shows the number of guests who drank Mirinda (M) and Coca-Cola (C) soda.

Mathematics

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Answers

2 parts
a

15\text{15}

b

2336\frac{23}{36}

Step-by-step solution

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Here are the solutions to the questions based on the Venn diagram.

The Venn diagram shows the number of guests who drank Mirinda (M) and Coca-Cola (C) soda.

  • Guests who took Mirinda only: 3m−63m - 6
  • Guests who took both Mirinda and Coca-Cola: 6
  • Guests who took Coca-Cola only: m+1m + 1
  • Guests who took neither: mm

The condition given is: "If those who took Mirinda but not Coca-Cola are equal to those who did not take Mirinda."

  1. Translate the given condition into an equation.

    "Those who took Mirinda but not Coca-Cola" is the number of guests who took Mirinda only, which is 3m−63m - 6.
    "Those who did not take Mirinda" includes guests who took Coca-Cola only and those who took neither. This is (m+1)+m(m + 1) + m.
    So, the equation is:

    3m−6=(m+1)+m3m - 6 = (m + 1) + m

  2. Solve the equation for mm.

    3m−6=2m+13m - 6 = 2m + 1

    Subtract 2m2m from both sides:

    3m−2m−6=13m - 2m - 6 = 1 m−6=1m - 6 = 1

    Add 6 to both sides:

    m=1+6m = 1 + 6 m=7m = 7

  3. Calculate the number of guests in each region using m=7m=7.

    • Guests who took Mirinda only: 3(7)−6=21−6=153(7) - 6 = 21 - 6 = 15
    • Guests who took both Mirinda and Coca-Cola: 6
    • Guests who took Coca-Cola only: 7+1=87 + 1 = 8
    • Guests who took neither: 7

  4. Answer part a).

    a) Find the number of guests who took Mirinda only.
    The number of guests who took Mirinda only is 3m−63m - 6.

    3(7)−6=21−6=153(7) - 6 = 21 - 6 = 15

    The number of guests who took Mirinda only is 15\boxed{\text{15}}.

  5. Answer part b).

    b) Find the probability that the next guest to graduate took only one type of soda.
    First, calculate the total number of guests:

    Total guests=(Mirinda only)+(Both)+(Coca-Cola only)+(Neither)\text{Total guests} = (\text{Mirinda only}) + (\text{Both}) + (\text{Coca-Cola only}) + (\text{Neither}) Total guests=15+6+8+7=36\text{Total guests} = 15 + 6 + 8 + 7 = 36

    Next, calculate the number of guests who took only one type of soda:

    Only one type=(Mirinda only)+(Coca-Cola only)\text{Only one type} = (\text{Mirinda only}) + (\text{Coca-Cola only}) Only one type=15+8=23\text{Only one type} = 15 + 8 = 23

    Finally, calculate the probability:

    P(Only one type)=Number of guests who took only one typeTotal number of guestsP(\text{Only one type}) = \frac{\text{Number of guests who took only one type}}{\text{Total number of guests}} P(Only one type)=2336P(\text{Only one type}) = \frac{23}{36}

    The probability that the next guest to graduate took only one type of soda is 2336\boxed{\frac{23}{36}}.

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