A basket contains 11 pieces of fruit: 4 apples, 5 oranges, and 2 bananas. Jonas takes a piece of fruit at random from the basket, and then Beth takes a piece at random. What is the probability that Jonas will get an orange and Beth will get an apple?
The probability that Jonas gets an orange is 5/11. Given that Jonas gets an orange, the probability that Beth gets an apple is 4/10. So the probability that Jonas gets an orange and Beth gets an apple is (5/11)*(4/10).
To find the probability that Jonas will get an orange and Beth will get an apple, we need to calculate the probability of each event happening and then multiply them together.
Step 1: Calculate the probability of Jonas getting an orange.
There are a total of 11 pieces of fruit in the basket. Out of these, there are 5 oranges. So the probability of Jonas getting an orange is 5/11.
Step 2: Calculate the probability of Beth getting an apple.
After Jonas takes a piece of fruit, there are now 10 pieces of fruit left in the basket. Out of these, there are 4 apples. So the probability of Beth getting an apple is 4/10, which can be simplified to 2/5.
Step 3: Multiply the probabilities together.
To find the combined probability of two independent events, we multiply the individual probabilities together:
(5/11) * (2/5) = 10/55, which can be simplified to 2/11.
Therefore, the probability that Jonas will get an orange and Beth will get an apple is 2/11.
To find the probability that Jonas will get an orange and Beth will get an apple, we need to consider the total number of possible outcomes and the number of favorable outcomes.
Total number of possible outcomes = Total number of fruits in the basket = 11
Number of favorable outcomes = Number of oranges in the basket * Number of apples in the basket = 5 * 4 = 20
Therefore, the probability that Jonas will get an orange and Beth will get an apple is:
Probability = Number of favorable outcomes / Total number of possible outcomes
= 20 / 11
= 1.818
However, probabilities should be expressed as fractions or decimals between 0 and 1, inclusive. So we can round it to the nearest decimal, which is approximately 0.82 or 82%.