Each of the 90 students in a class speak at least Igbo or Hausa. If 56 students speak Igbo and 50 speak Hausa, find the probability that a student selected at random from the class speaks Igbo only.
\(\frac{28}{45}\)
\(\frac{4}{9}\)
\(\frac{8}{45}\)
\(\frac{1}{9}\)
Correct answer is B
Let the number of candidates that speak both Igbo and Hausa = x
The number that speaks Igbo only = 56 - x
The number that speaks Hausa only = 50 - x
56 - x + x + 50 - x = 90
106 - x = 90
x = 16
P(Igbo only) = \(\frac{56 - 16}{90} = \frac{4}{9}\)