Understanding 'and' and 'or' in probability is really important for learning about combined events.

1. 'And' (Intersection):

• We use 'and' when both events need to happen.
• For example, let's say we want to know the chances of rolling a 4 on a die and flipping heads on a coin.
• To find this probability, we do the following calculation:
  • ( P(A \cap B) = P(A) \times P(B) = \frac{1}{6} \times \frac{1}{2} = \frac{1}{12} )

2. 'Or' (Union):

• We use 'or' when at least one of the two events occurs.
• For example, let's find the chances of rolling a 4 or flipping heads.
• We calculate it like this:
  • ( P(A \cup B) = P(A) + P(B) - P(A \cap B) = \frac{1}{6} + \frac{1}{2} - \frac{1}{12} = \frac{5}{12} )

When you understand these ideas, it helps you figure out the chances of more complicated events correctly.