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.
-
A.
(frac{28}{45}) -
B.
(frac{4}{9}) -
C.
(frac{8}{45}) -
D.
(frac{1}{9})
Correct Answer: Option B
Explanation
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})