There are 4 apples and 6 pears I. A fruit basket. What is the probability of randomly selecting a pear, not replacing it then selecting an apple?
There are a total of 10 fruits in the basket.
The probability of selecting a pear on the first draw is 6/10.
After selecting a pear, there are 9 fruits left in the basket, including 4 apples.
The probability of then selecting an apple on the second draw is 4/9.
To find the probability of both events happening together, we multiply the probabilities:
6/10 * 4/9 = 24/90 = 4/15
Therefore, the probability of randomly selecting a pear, not replacing it, and then selecting an apple is 4/15.
To calculate the probability of randomly selecting a pear, not replacing it, and then selecting an apple, we need to consider the number of possible outcomes and the number of favorable outcomes.
Step 1: Calculate the probability of selecting a pear first.
The total number of fruits in the basket is 4 apples + 6 pears = 10.
The probability of selecting a pear on the first draw is 6 pears (favorable outcomes) out of 10 fruits (possible outcomes), which can be written as 6/10 or 3/5.
Step 2: Calculate the probability of selecting an apple after not replacing the pear.
After removing the pear from the basket, there are now 9 fruits remaining (3 apples + 6 pears).
The probability of selecting an apple on the second draw is 3 apples (favorable outcomes) out of 9 fruits (possible outcomes), which can be written as 3/9 or 1/3.
Step 3: Calculate the combined probability.
To find the probability of both independent events occurring, we multiply the probabilities from the previous steps.
Probability of selecting a pear first and then an apple = (3/5) × (1/3) = 3/15 = 1/5.
Therefore, the probability of randomly selecting a pear, not replacing it, and then selecting an apple is 1/5 or 20%.