Question

The likehood of an event occurring may be described as certain more likely equally likely less or impossible

Answer 1

PART A

To find the probability that a single pencil that is drawn from the box is black, we simply have to compare the number of black pencils in the box to the total number of pencils in the box.

Number of black pencils = 0 (there are no black pencils in the box)

Total number of pencils = 25

Now the probability of drawing a black pencil is equal to:

`\frac{Number\text{ of black pencils}}{\text{Total number of pencils}}`

This is equal to:

`\frac{Number\text{ of black pencils}}{\text{Total number of pencils}}=(0)/(25)\text{ = 0}`

Therefore, there is a zero probability of drawing a black pencil from the box.

This can be otherwise stated as: it is impossible to draw a black pencil from the box.

This makes sense because there is no black pencil in the box. So, it is not possible that any pencil drawn from the box will be black.

PART B

To compare the likelihood of drawing a red pencil to that of drawing a blue pencil, we must first calculate the probability of drawing a red pencil, and then also separately calculate the probability of drawing a blue pencil. After which we will then compare the two values of the probabilities.

To find the probability that a single pencil that is drawn from the box is red, we simply have to compare the number of red pencils in the box to the total number of pencils in the box.

Number of red pencils = 11

Total number of pencils = 25

Now the probability of drawing a red pencil is equal to:

`\frac{Number\text{ of red pencils}}{\text{Total number of pencils}}`

This is equal to:

`\frac{Number\text{ of red pencils}}{\text{Total number of pencils}}=(11)/(25)`

Now, to find the probability that a single pencil that is drawn from the box is blue, we also simply have to compare the number of blue pencils in the box to the total number of pencils in the box.

Number of blue pencils = 11

Total number of pencils = 25

Now the probability of drawing a blue pencil is equal to:

`\frac{Number\text{ of blue pencils}}{\text{Total number of pencils}}`

This is equal to:

`\frac{Number\text{ of blue pencils}}{\text{Total number of pencils}}=(11)/(25)`

Now, as we can see, the probability of drawing a red pencil (11/25) is exactly the same as the probability of drawing a blue pencil (11/25).

Therefore, by comparison, this means that the probability of drawing a red pencil and the probability of drawing a red pencil are equally likely.

This makes sense since we have just many red pencils in the box as there are blue pencils.