Question

In a bag of fruits, there are 5 apples and 3 pears. If I pick a fruit and do not replace it, then I pick another, what is the probability that:

(1) Both are apples.
(2) The first is a pear and the second an apple.
(3) One is an apple and the other is a pear.
A. (1) 1/7, (2) 5/24, (3) 5/24
B. (1) 1/7, (2) 3/24, (3) 5/24
C. (1) 5/24, (2) 3/24, (3) 5/24
D. (1) 5/24, (2) 5/24, (3) 3/24

Answer 1

The probability of picking 2 apples is 5/14, the probability of picking a pear and then an apple is 15/56, and the probability of picking one apple and one pear is 15/28.

Step-by-step explanation:

To find the probability, we need to consider the total number of fruits in the bag and the number of each type of fruit.

1. 
   
3. The probability of picking an apple on the first try is 5/8. Since we do not replace the fruit, the probability of picking another apple on the second try is 4/7. So, the probability of both being apples is (5/8) * (4/7) = 20/56 = 5/14.
4. 
   
6. The probability of picking a pear on the first try is 3/8. Then, the probability of picking an apple on the second try is 5/7. So, the probability of the first being a pear and the second being an apple is (3/8) * (5/7) = 15/56.
7. 
   
9. This case includes two possibilities: picking an apple first and a pear second or picking a pear first and an apple second. The probability of picking an apple first and a pear second is (5/8) * (3/7) = 15/56. The probability of picking a pear first and an apple second is (3/8) * (5/7) = 15/56. So, the probability of one being an apple and the other being a pear is (15/56) + (15/56) = 30/56 = 15/28.