Final answer:
The probability of choosing an apple first and then an orange from a bag with 6 bananas, 2 oranges, and 7 apples without replacement is 1/15.
Step-by-step explanation:
To calculate the probability of choosing an apple first from the bag and then an orange, you would need to calculate the probability of each event separately and then multiply them together because you are dealing with independent events.
There are a total of 6 bananas, 2 oranges, and 7 apples in the bag, making up a total of 15 fruits.
Probability of choosing an apple first = Number of apples / Total number of fruits
P(Apple first) = 7 apples / 15 fruits = 7/15.
Without replacement means the apple is not put back into the bag. Thus, after taking out an apple, there are 14 fruits left.
Probability of choosing an orange second = Number of oranges / Remaining number of fruits after the first draw
P(Orange second) = 2 oranges / 14 fruits = 1/7.
The combined probability of both events happening in sequence is found by multiplying the two probabilities:
Probability of choosing an apple first and then an orange = P(Apple first) × P(Orange second) = (7/15) × (1/7) = 1/15.