EXAMPLE 1 Independent and Dependent Events Tell whether the events are independent or dependent. SOLUTION You randomly draw a number from a bag. Then you randomly draw a second number without putting the first number back. b. You roll a number cube. Then you roll the number cube again. a. The result of the first roll does not affect the result of the second roll, so the events are independent. There is one fewer number in the bag for the second draw, so the events are dependent. SOLUTION

EXAMPLE 2 Standardized Test Practice SOLUTION The tosses are independent events, because the outcome of a toss does not affect the probability of the next toss resulting in a win. So the probability of each event is. 1 25

EXAMPLE 2 Standardized Test Practice P ( win and win ) = P ( win ) P ( win ) = ANSWER The probability of two winning tosses in a row is The correct answer is A =

GUIDED PRACTICE for Examples 1and 2 In Exercises 1 and 2, tell whether the events are independent or dependent. Explain your reasoning. 1. You toss a coin. Then you roll a number cube. You randomly choose 1 of 10 marbles. Then you randomly choose one of the remaining 9 marbles. 2. The coins toss does not affect the roll of a dice, so the events are independent. ANSWER There is one fewer number in the bag for the second draw, so the events are dependent. ANSWER

GUIDED PRACTICE for Examples 1and 2 3. You toss a coin twice. Find the probability of getting two heads. P( head and head ) = P( head ) P( head ) = 1 4 or 25% = The tosses are independent events, because the outcome of a toss does not affect the probability of the next toss ANSWER