In a hotel, the breakfast is a choice between yam (Y) or plantain (P) or both....

In a hotel, the breakfast is a choice between yam (Y) or plantain (P) or both. The Venn diagram shows the choices made by 25 guests of the hotel.

(a) Find the value of x;

(b) What is the probability that a guest chosen at random chose only one of the two?

(a)

(U = 25)

(therefore (2x + 1) + x + (x – 2)^{2} = 25)

(x^{2} – 4x + 4 + x + 2x + 1 = 25)

(x^{2} – x + 5 – 25 = 0)

(x^{2} – x – 20 = 0)

(implies x^{2} – 5x + 4x – 20 = 0)

(x(x – 5) + 4(x – 5) = 0)

(implies text{x = -4 or 5})

But x cannot be negative in this case, hence, x = 5.

(b) Number of guests that selected just one meal = (2x + 1 + x^{2} – 4x + 4)

(x^{2} – 2x + 5 = 5^{2} – 2(5) + 5 = 25 – 10 + 5 = 20)

Probability of selecting a person who picked one meal = (frac{20}{25} = frac{4}{5}).

In a hotel, the breakfast is a choice between yam (Y) or plantain (P) or both….