Understanding Independent and Dependent Events in Probability

Let’s break down how to tell the difference between independent and dependent events in probability.

1. Independent Events:

   • These are events where one outcome doesn’t change the other.
   • For example, think about rolling a die and flipping a coin.
   • The chances of getting a certain number on the die do not change if you get heads or tails on the coin.
   • The math for this is:
     ( P(A \text{ and } B) = P(A) \times P(B) )
     This means you just multiply the probabilities of each event happening.

2. Dependent Events:

   • These are events where one outcome does change the other.
   • For instance, if you draw cards from a deck and don’t put the first card back, the second card you pick is affected by what you drew first.
   • The math for this looks like:
     ( P(A \text{ and } B) = P(A) \times P(B | A) )
     Here, ( P(B | A) ) shows the probability of event B happening after event A has already happened.

By understanding these differences, you can better grasp how the outcomes of different events relate to each other in probability.