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# Probability and Statistics

# Independent and Dependent Events Exercises

### Example 1

Determine whether the event is independent or dependent:

Rolling 5 on a die and flipping tails on a coin.

### Example 2

Determine whether the event is independent or dependent:

Flipping heads on a coin and then flipping tails on that same coin.

### Example 3

Determine whether the event is independent or dependent:

Drawing a king from a deck of cards and then, without replacing the king, drawing a queen from the same deck of cards.

### Example 4

Using the formal definition of independence, determine whether events *A* and *B* are independent or dependent.

Rolling two dice, with

Event *A*: Rolling 1 on the first die.

Event *B*: The dice summing to 7.

### Example 5

Using the formal definition of independence, determine whether events *A* and *B* are independent or dependent.

Flip three coins, with

Event *A*: The first two coins are heads.

Event *B*: There are at least two heads among the three coins.

### Example 6

Using the formal definition of independence, determine whether events *A* and *B* are independent or dependent.

Given two spinners (this sort of thing) that each have the numbers 1, 2, and 3 (in place of the colors), we spin two numbers.

Event *A*: Spinning an odd number on the first spinner.

Event *B*: The sum of the two numbers being odd.

Okay, so you ready to take this exercise for a spin? It even still has that "new problem smell"...