Vocabulary: Remember . . .Independent Events– when one event does ____________________ affect the outcome of another event. For example, when two coins are tossed, the result of the 2nd coin does NOT depend on what the first coin lands on. Both coins have a 50% chance of landing on heads (or tails) no matter what. Dependent Events– when the outcome of one event _________________________________ on the outcome of the other event. For example, picking two Aces in a row from a standard deck of cards WITHOUT replacing the first card. Let’s work this out . . .

Math-8 NOTES DATE: ______/_______/_______What: probability of compound, dependent events

Why: To calculate the probability of compound, dependent events.

NAME:

Scenario Dependent or Independent?

1. Out of a bag of 20 marbles, calculating the probability of picking a red marble, setting it aside, and picking a green marble.

2. When flipping a coin and rolling a die, calculating the probability of getting heads and a 4.

3. Out of a bucket of tootsie pops, calculating the probability of picking a cherry, putting it back in the bucket, and then picking an orange.

4. When flipping three coins at once, calculating the probability of getting three heads in a row.

5. From a standard deck of cards, calculating the probability of picking a red Queen, keeping it, and then picking a black Jack.

6. From a standard deck of cards, calculating the probability of picking a diamond, replacing the card, and picking the six of hearts.

PROBABILITY TRIALS(compound, dependent events)

1) Trial One: Tootsie Pop Pick (2 Picks)Out of 20 Trials (2 picks each), how many times will a grape get picked twice – P(grape and grape)? The pops will NOT be replaced after each pick.-Probability : -What is our percentage chance? - Results of experiment:

- Did the results match what should have happened? 2) Trial Two: Picking a Heart and a Black Card After 20 trials, how many times will a heart AND a black card be chosen (first card will NOT be replaced) -- P(heart and black card)?

-Probability : -What is our percentage chance? - Results of experiment:

- Did the results match what should have happened? 3) Trial Three: Picking an Ace and a King After 20 trials, how many times will an Ace and a King be picked (first card will NOT be replaced) – P (Ace and a King)?

-Probability : -What is our percentage chance? - Results of experiment:

- Did the results match what should have happened?

Sample compound, dependent event problems . . .

SCENARIO ANSWER1) From a standard deck of cards,

what is the probability of picking a red Queen, setting the card aside, and then picking a diamond?

2) There are 3 orange, 4 cherry, and 5 grape starburst in a bag. You will pick two in a row without replacing any. What is the probability that you will choose two oranges in a row?

3) There are 2 orange, 3 cherry, and 4 chocolate pops in a bag. You will pick two in a row without replacing any. What is the probability that you will pick a chocolate and a cherry?

4) Erik is one out of 20 total students in his class. What is the probability that Erik will be one of two students randomly chosen to have lunch with Mr. Runfola?

5) There are 12 girls and 10 boys in

Ms. Dyson’s class. If all the students’ names are put into a hat and Ms. Dyson randomly chooses two names (without replacing them), what is the probability that the names chosen will be a boy and a girl?

Math-8 practice“independent and dependent probability”

DATE: ______/_______/_______NAME:_____________________________________________________________________________Probability of Independent and Dependent Events

Independent Events:

A number cube is rolled and a coin is tossed. Find each probability.

1. P(2 and heads) 2. P(2 or 3 and tails)

3. P(greater than or equal to 3 and heads) 4. P(less than 6 and tails)

5. P(1 and heads or tails) 6. P(10 and tails)

There are 5 yellow marbles, 1 purple marble, 3 green marbles, and 3 red marbles in a bag. Once a marble is drawn,

it is replaced. Find the probability of each outcome.

7. P(purple, then red) 8. P(red, then green)

9. P(green, then green) 10. P(red, then red)

11. P(purple, then green) 12. P(red, then yellow)

Dependent Events

There are 4 yellow marbles, 3 purple marbles, 1 green marble, and 1 white marble in a bag. Once a marble is drawn, it is not replaced. Find the probability of each outcome.

13. P(purple, then white) 14. P(white, then green)

15. P(purple, then purple) 16. P(yellow, then yellow)

17. P(yellow, then purple) 18. P(green, then white)

Determine whether or not the following events are Independent or Dependent.

19. Flipping two coins.________________

20. Choosing two marbles from a bag, but not replacing the first one.________________

21. Rolling a number cube and spinning a spinner.________________

22. Picking two socks out of a drawer, but not replacing the first one.________________

23. Choosing two marbles from a bag, with the first one replaced.________________

24. Choosing two students from a class to be the SCA class representative.________________

25. Picking a card from a standard deck of cards.________________