Basket A contains 4 apples, 6 oranges, and 2 lemons. Basket B contains 5 apples, 4 oranges, and 6 lemons. You are to get two fruits from each basket. What is the probability of getting 2 oranges from basket A and then 1 apple and 1 lemon from basket B?
Well, to find the probability, we need to first calculate the total number of possible outcomes.
In basket A, there are a total of 12 fruits (4 apples + 6 oranges + 2 lemons). To get 2 oranges, we need to calculate the probability as (number of ways to get 2 oranges) divided by (total number of possible outcomes).
The number of ways to get 2 oranges from basket A can be calculated using combinations: C(6, 2) = 6! / (2! * (6-2)!) = 15.
So the probability of getting 2 oranges from basket A is 15 / 12 = 5 / 4.
Moving on to basket B, there are a total of 15 fruits (5 apples + 4 oranges + 6 lemons). To get 1 apple and 1 lemon, we need to calculate the probability as (number of ways to get 1 apple) * (number of ways to get 1 lemon), divided by (total number of possible outcomes).
The number of ways to get 1 apple from basket B is 5, and the number of ways to get 1 lemon is 6.
So the probability of getting 1 apple and 1 lemon from basket B is (5 * 6) / 15 = 2 / 3.
Since we want both events to happen (2 oranges from basket A and 1 apple + 1 lemon from basket B), we need to multiply the probabilities together.
The final probability is thus (5 / 4) * (2 / 3) = 10 / 12 = 5 / 6.
So the probability of getting 2 oranges from basket A and then 1 apple and 1 lemon from basket B is 5 / 6.
To calculate the probability, we need to consider the total number of possibilities and the favorable outcomes.
In basket A, there are a total of 4 apples, 6 oranges, and 2 lemons. We want to get 2 oranges, so the probability of getting the first orange would be 6/12 (since there are 6 oranges out of a total of 12 fruits remaining). After taking one orange, we have 5 oranges left in the basket.
The probability of getting the second orange would then be 5/11 (since there are 5 oranges left out of a total of 11 fruits remaining).
Now, we move on to basket B. We need to pick 1 apple and 1 lemon. In basket B, there are 5 apples, 4 oranges, and 6 lemons. The probability of getting the apple would be 5/15 (since there are 5 apples out of a total of 15 remaining fruits). After taking one apple, we have 4 apples left in the basket.
The probability of getting the lemon would then be 6/14 (since there are 6 lemons left out of a total of 14 remaining fruits).
To find the probability of all these events happening in order, we multiply the individual probabilities together:
Probability = (6/12) * (5/11) * (5/15) * (6/14)
Simplifying this expression, we get:
Probability = 25/924
Therefore, the probability of getting 2 oranges from basket A, and 1 apple plus 1 lemon from basket B, is 25/924.
A ... there are 12C2 ways of selecting two fruits
... 6C2 ways of selecting two oranges
B ... there are 15C2 ways of selecting two fruits
... any of 5 apples, paired with any of 6 lemons ... 5 * 6 possibilities