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JAMB Mathematics 2017 Paper

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Question : 3

Total: 44

If U = {x : x is an integer and 1 ≤ x ≤ 20 }

E1 = {x: x is a multiple of 3}

E2 = {x: x is a multiple of 4} and an integer is picked at random from U, find the probability that it is not in E2

$\frac{3}{4}$
$\frac{3}{10}$
$\frac{1}{4}$
$\frac{1}{20}$

Solution:

Concept:

The probability that an integer picked is not in

E_2

is found by subtracting the probability of

E_2

from 1.

Explanation:

The universal set is

U = \{1, 2, 3, \dots, 20\}

, so the total number of outcomes is

20

.

E_2 = \{x : x \text{ is a multiple of } 4\}

from

U

.

Thus,

E_2 = \{4, 8, 12, 16, 20\}

, which contains

5

elements.

So,

P(E_2) = \frac{\text{number of elements in } E_2}{\text{total elements in } U} = \frac{5}{20}

.

Therefore,

P(\text{not in } E_2) = 1 - \frac{5}{20} = \frac{20 - 5}{20} = \frac{15}{20}

.

Simplifying,

P(\text{not in } E_2) = \frac{3}{4}

.

Answer:

\frac{3}{4}

(Option A).

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