Back to Apply the general Multiplication Rule — Problem 3 · Task Set 25

Exercises: Apply the General Multiplication Rule

Work through each section in order. Use the general Multiplication Rule, $P(A \text{ and } B) = P(A) \cdot P(B \mid A)$, for joint probabilities. For draws WITHOUT replacement, remember that BOTH the favorable count and the total shrink after the first draw. On a tree diagram, MULTIPLY along a path and ADD across paths. Leave fractions exact unless told otherwise.

Grade 11·21 problems·~35 min·Common Core Math - HS Statistics and Probability·group·hss-cp-b-8

Work through problems with immediate feedback

Warm-Up: Product Rule and Conditional Probability

These problems review the prior ideas the new rule builds on.

The general Multiplication Rule has two symmetric forms: $P(A) \cdot P(B \mid A)$ and $P(B) \cdot P(A \mid B)$ . What is true about these two expressions?

They always give the same value, the joint probability $P(A \text{ and } B)$ .

They give different answers, so you must memorize which to use.

They are equal only when $A$ and $B$ are independent.

The first is the joint probability and the second is the conditional probability.