Word Problems Strategy Guide Chapter 7

[franalej]

Example 3 ask for a die rolled (A) and coin flipped once (B). The question is what is the probability that either the die will come up 2 or 3, OR the coin will land heads? The explanation offered by the book assumes that since the die and the coin are independent events the formula of P(A) + P(B) - P(A)P(B) must be applied to find P(A) OR P(B). I don't understand why this formula has to be used and not the one without the P(A)P(B), because the die and the coin even though are independent are mutually exclusive as well. A die cannot be a coin. Thanks.

[tommywallach]

Hey Franalej,

This is a common misunderstanding of independence. Independence relates to issues within a single event structure (i.e. a die or a coin, separately) that could also be dependent. For example, each roll of a die is independent. But if I pull a marble from a hat and don't replace it, the next pull is NOT independent from the first pull.

But two separate events like this are ALWAYS independent. The thing to remember is this: If there's a 50% chance of rain tomorrow and a 50% chance of me eating a turkey sub, does that mean there's a 100% chance of one OR the other happening? No! Of course not! This is why the simple addition doesn't work. It doesn't even make sense!

Clear?

-t