Question

A number is selected from the set {1, 2, 3, 4, 5, 6, 7, 8}. The probability that it is a root of the equation x² – 6x + 8 = 0, is ________.

Answer 1

Total number of outcomes = 8

The given equation is x² – 6x + 8 = 0.

x² – 6x + 8 = 0

⇒ x² – 4x – 2x + 8 = 0

⇒ x(x – 4) – 2(x – 4) = 0

⇒ (x – 2)(x – 4) = 0

⇒ x – 2 = 0 or x – 4 = 0

⇒ x = 2 or x = 4

So, the roots of the given equation are 2 and 4.

Favourable number of cases = Number of roots of the given equation = 2

∴ Probability that the selected number is a root of given equation = $\frac{\mathrm{Favourable}\mathrm{number}\mathrm{of}\mathrm{cases}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{cases}}=\frac{2}{8}=\frac{1}{4}$

A number is selected from the set {1, 2, 3, 4, 5, 6, 7, 8}. The probability that it is a root of the equation x² – 6x + 8 = 0, is $\underline{\frac{1}{4}}$.