Theory question 105
ProbabilityIn a hotel the breakfast menu 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?
Show the model answer
Model answer
(a) (2x + 1) + x + (x − 2)2 = 25
x2 − x − 20 = 0, (x − 5)(x + 4) = 0
x = 5 (x cannot be negative)
(b) P only = 11, Y only = 9, so 20 guests chose only one
Probability = 20/25 = 4/5
Explanation
The three regions of the Venn diagram add up to the 25 guests.