Question

2. Consider picking a number between 1 - 20.Part A: To determine the probability of picking an even number or a multiple of three, onewould use theoretical probability or empirical probability? Justify your answer.Part B: Determine the probability of picking an even number or a multiple of three.

Answer 1

PartA

The probability of picking an even number or a multiple of three is a theoretical probability because the sample space(the possible outcome) can easily be gotten and hence the probability of the event can be calculated using the formula

Part B

Let the probability of picking an even number =P(A)

probability of picking a multiple of three =P(B)

hence using theoretical probability

`\begin{gathered} P(A)=\frac{Number\text{ of even number }}{Total\text{ number}} \\ \text{Even number betw}een1-20=10\text{ } \\ \text{total number=20} \end{gathered}`

Hence

`P(A)=(10)/(20)=(1)/(2)`

Multiples of 3 between 1-20 are 3, 6,9,12,15,18=6

`P(B)=\frac{Numbers\text{ of multiple of 3}}{total\text{ number}}=(6)/(20)=(3)/(10)`

Then, the probability of P(A) or P(B) is the addition of the individual probability

`(1)/(2)+(3)/(10)=(4)/(5)`

Therefore the probability of picking an even number or a multiple of three is 0.8