Question

A jar contains twelve red marbles numbered from 1 to 12 and six blue marbles numbered from 1 to 6. A marble is drawn at random from the jar. Find the probability of the given event. a) The marble is r

Answer 1

The probability of randomly drawing a red marble from the jar is
`\( (2)/(3) \)`or approximately 0.6667.

Step-by-step explanation:

To calculate the probability, we use the formula:

`\[ P(\text{Event}) = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Outcomes}} \]`

In this case, the event is drawing a red marble, and there are 12 red marbles in the jar. The total number of marbles in the jar is the sum of red and blue marbles, which is
`\(12 + 6 = 18\).`Therefore, the probability of drawing a red marble is:

`\[ P(\text{Red}) = (12)/(18) = (2)/(3) \]`

Alternatively, this can be expressed as a decimal by dividing 2 by 3, resulting in approximately 0.6667.

Understanding probability is crucial for making informed predictions in various scenarios. In this context, the probability of drawing a red marble provides insights into the likelihood of a specific outcome. The fraction
`\( (2)/(3) \)` indicates that, on average, two out of every three draws would be red marbles, assuming the marbles are well-mixed and the drawing process is truly random.