Compound Events: Independent and Dependent

Compound Probability The probability of two or more events occurring (for example – rolling a 6 and landing on heads) We need to find all possible combinations of outcomes

Possible Outcomes Outcomes H T H T H T H T H T H T 12 outcomes 1 2 3 4 5 6 H T H T H T H T H T H T 1H 1T 2H 2T 3H 3T 4H 4T 5H 5T 6H 6T 12 outcomes

Possible Outcomes Roll a Die Possible Outcomes Flip a Coin 1 2 3 4 5 6 H T 6  2 12 possible outcomes

Definition  Possible Outcomes Possible Outcomes Flip a Coin Possible Outcomes Roll a Die Possible Outcomes Flip a Coin 

Possible Outcomes Roll a Die Possible Outcomes Spin a Spinner Example Possible Outcomes Roll a Die Possible Outcomes Spin a Spinner 6  4 24 possible outcomes

Possible Outcomes Pick a Card Possible Outcomes Flip a Coin Example Possible Outcomes Pick a Card Possible Outcomes Flip a Coin 1 1 2 2 3 3 4 4 4  2 8 possible outcomes

Possible Outcomes Pick a Marble Possible Outcomes Roll a die Example Possible Outcomes Pick a Marble Possible Outcomes Roll a die 4  6 24 possible outcomes

2   6 4 48 possible outcomes Example Possible Outcomes Pick a Marble Possible Outcomes Roll a die Possible Outcomes Flip a Coin 2  4 6  48 possible outcomes

Definition Independent event Example: the result of the first event does not affect the other event Example: picking an M&M and putting it back in the bag before picking another (by putting the M&M back, there are still the same number of M&Ms in the bag for the second pick)

the result of the first event does affect the other event Definition Dependent event the result of the first event does affect the other event Example: picking an M&M and not putting it back in the bag before picking another (keeping the M&M changes the total number of M&Ms in the bag, and may change the number of favorable outcomes)

Independent or Dependent? Students got to pick their favorite color of shoes. They had to write a paragraph about their choice. Their teacher told them it does not matter what their classmates pick. Adam, Ciara, and Ryan picked the same color of shoes. Is this an independent or dependent event? Independent event What Adam picks does not limit what the rest of the class can choose.

Independent or Dependent? High school students are making tessellation projects. The teacher wants each design to be a completely different picture. The teacher does not want any duplicates. Cassidy gets her picture approved first, followed by Bill. Is this an independent or dependent event? Dependent event What Cassidy chooses, Bill can not choose. Bill is effected.

Independent or Dependent? Tom picks a marble at random. He returns the marble to the pile and then picks another marble at random. Is this an independent or dependent event? Independent event What Tom chooses the first time does not effect his second choice. Because he puts back his first choice, he can still choose any of the four colored marble on the second draw.

Independent or Dependent? Stephanie spins the spinner twice. Is this an independent or dependent event? Independent event. What Stephanie spins the first time does not effect her second spin.

Independent or Dependent? Jake picks a card. He keeps the card and then picks another one. Is this an independent or dependent event? 1 2 3 4 Dependent event The card he keeps from his first choice he can not pick the second time.

Definition Compound Probability To find the probability of two or more events happening, find the probability of each and multiply the answers

 Example (Independent Events) 1 1 4 6 1 P(1,red) = 24 You roll a die and spin the spinner. What is the P(1,red)? (the probability of rolling a 1 and spinning a red) Probability of spinning red Probability of rolling a 1 1 4  1 6 1 24 P(1,red) =

Example (Independent Events) Carlos spins the spinner twice. What is the probability of spinning an orange and then a brown? P(brown) P(orange) 2 5 2 5  4 25 P(orange, brown) =

Example (Independent Events) Ben picks a card. He puts it back and picks another card. What is the probability that he picks a green card twice? P(green) P(green) 4 5 4 5  16 25 P(green, green) =

Example (Independent Events) Jen flips a coin. What is the probability that she gets a tail both times? P(tails) P(tails) 1 2 1 2  1 4 P(orange, brown) =

Example (Dependent Events) Carson picks a marble at random. He does not put the first marble back. Again he picks another marble. What is the probability that he picks a purple and then a purple? P(purple) P(purple) 3 8 2 7  6 56 3 28 P(purple, purple) =

Example (Dependent Events) Ty picks a card. He keeps it and then picks another. What is the probability that he picks a 5 and then a 6? 5 6 7 8 P(5) P(6) 1 4  1 3 1 12 P(5,6) =

Example (Dependent Events) A bowl of fruit is on the table. It contains 4 apples, 6 oranges, and 5 bananas. Justin and Logan come home from school and randomly grab one fruit each. What is the probability that both grab apples? P(apple) P(apple) 4 15 3 14  12 210 2 35 P(apple,apple) =