Abag contains 15 dark chocolates, 16 caramel chocolates, and 19 milk chocolates. the probability that amber’s teacher distributes the chocolates among her students is 0.4. if the teacher offers amber a chocolate from the bag, the probability that she randomly picks either a caramel chocolate or a dark chocolate

The answer is 31/125 ≈ 0.25.

To calculate this, we will use both addition rule and multiplication rule.
The addition rule is used to calculate the probability of one of the events from multiple pathways. If you want that only one of the events happens, you will use the addition rule. In this method, the possibilities of each event are added. So, we will use the addition rule to calculate the probability that the teacher randomly picks either a caramel chocolate (1st event) or a dark chocolate (2nd event):
1. There are 16 caramel chocolates out of 50 chocolates in total. Thus, the probability that a caramel chocolate is picked is 16/50.
2. There are 15 chocolates out of 50 chocolates in total. Thus, the probability that a caramel chocolate is picked is 15/50.
ADDITION RULE:
16/50 + 15/50 = 31/50
The probability that teacher picks either a caramel chocolate or a dark chocolate is 31/50.

The multiplication rule calculates the probability that both of two events will occur. In this method, the possibilities of each event are multiplied. So, we will use the multiplication rule to calculate the probability that the teacher distributes the chocolates among students (1st event) and that  she randomly picks either a caramel chocolate or a dark chocolate (2nd event):

1. The probability that the teacher distributes the chocolates  among students is 0.4 = 4/10.

2. The probability that teacher picks either a caramel chocolate or a dark chocolate is 31/50.

MULTIPLICATION RULE:

4/10 × 31/50 = 124/500 = 31/125 ≈ 0.25