Question

Fill in the blank The probability of a chance event is a number between 0 and that expresses the likelihood of the event occurring A. 1 10 B. 1/2 C. 100 D. 1

Answer 1

Let's assume we want to know the probability of an event. We are going to label successful case to the situation where the event happens and unsuccessful case to the situation where it doesn't happen. Then the probability of a successful case i.e. the probability that the event happens is given by:

`\frac{\text{posible successful cases}}{\text{all posible cases}}=\frac{\text{posible successful cases}}{\text{posible successful and unsuccessful cases}}`

For example if we want to roll a dice and see the probability of getting a 2 we have:

- One successful case: rolling a 2

- 5 unsuccessful cases: rolling 1, 3, 4, 5 or 6.

Then the probability of rolling a 2 i.e. the probability of the event is:

`(1)/(1+5)=(1)/(6)`

Since we have that:

`\text{all posible cases}=\text{posible successful and unsuccessful cases}`

Then the quotient:

`0\leq\frac{\text{posible successful cases}}{\text{all posible cases}}\leq1`

So the probability P given by this quotient meets:

`0\leq P\leq1`

And the answer to this question is option D.