Question

A basket contains 10 fruits of which 3 are rotten. If one fruit is drawn from the basket, then the probability that the fruit drawn is not rotten is ____. (1) \(4 / 5\) (2) \(4 / 5\) (3) \(7 / 10\) (4) \(3 / 10\)

Short answer

Answer: \(7 / 10\)

Step-by-step solution

Understanding the problem

The basket contains 10 fruits, out of which 3 are rotten. In this case, if one fruit is drawn from the basket without looking, we need to find the probability that the fruit drawn is not rotten.

Determine the total number of outcomes

The total number of outcomes in this case is equal to the total number of fruits in the basket. This is because any of the fruits can be picked. Since there are 10 fruits, the total number of outcomes is 10.

Determine the number of favorable outcomes

The favorable outcomes are the outcomes where a non-rotten fruit is picked. To find the number of favorable outcomes, subtract the number of rotten fruits from the total number of fruits. This gives 10 - 3 = 7 favorable outcomes.

Apply the formula of probability

The probability of an event is calculated as the ratio of the number of favorable outcomes to the total number of outcomes. By substituting the number of favorable and total outcomes into the probability formula, the probability of picking a non-rotten fruit is 7 / 10. So the correct answer is (3) \(7 / 10\).

Key concepts

Favorable Outcomes

In probability, a **favorable outcome** is any outcome that aligns with the specific event we're interested in. In our fruit basket example, we're concerned with picking a fruit that is not rotten. To find the number of favorable outcomes, we need to count all such instances where the event can occur successfully. In this case:

• Total fruits = 10
• Rotten fruits = 3

To calculate the number of favorable outcomes, we subtract the rotten ones from the total, resulting in 10 - 3 = 7 favorable outcomes. These seven fruits are the non-rotten ones, making them desirable for our event.

Total Outcomes

**Total outcomes** refer to all possible outcomes that could happen in an event, whether they're favorable or not. For our example of drawing a fruit from a basket, the total possible outcomes are simply the total number of fruits we have, regardless of their condition. This means considering every single fruit as a potential pick:

• Total number of outcomes = Total fruits = 10

Understanding the concept of total outcomes helps in forming the basis for calculating probability, as it represents the denominator in the probability formula. Every outcome is equally likely, and we assume we have complete knowledge of every possible scenario.

Probability Formula

The **probability formula** is a simple yet powerful tool that helps us calculate the likelihood of an event occurring. It is expressed as:\[P( ext{Event}) = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Outcomes}}\]This formula gives us a fraction that represents the chance of the event happening. In our fruit basket scenario, the favorable outcomes are drawing a non-rotten fruit, which we calculated to be 7. Our total number of outcomes, or potential draws, is 10. Plugging these values into the formula, the probability is:\[P( ext{Non-rotten fruit}) = \frac{7}{10}\]This fraction, \(\frac{7}{10}\), or 0.7, indicates a 70% chance of picking a non-rotten fruit. The probability formula allows us to make informed predictions based on known conditions, and it's a cornerstone of understanding probability.