PART 3 TREE DIAGRAMS HOMEWORK DAY 3 HW

PART 3 TREE DIAGRAMS HOMEWORK: DAY 3 HW (1, 2, 4)

BY THE TIME I WALK OUT OF CLASS TODAY • I can draw a tree diagram to calculate the probability an event will occur.

EXAMPLE You flip the same coin 3 times in a row. H (0. 5 ) We can draw a tree diagram H to show all the possible (0. 5) outcomes. T (0. 5) H (0. 5) T (0. 5 ) H (0. 5) H T (0. 5) T H (0. 5) T (0. 5) 0. 125 0. 125

KEY FEATURES Every time the tree branches, those probabilities have to add up to 100%. H (0. 5 ) H (0. 5) T (0. 5 ) T (0. 5) H T (0. 5) T H (0. 5) T (0. 5) 0. 125 0. 125

KEY FEATURES Every time the tree branches, those probabilities have to add up to 100%. The probabilities at the bottom are found by multiplying the percentages along the path. H (0. 5) H (0. 5) T H (0. 5) T (0. 5) H T (0. 5) T H (0. 5) T (0. 5) 0. 125 0. 125

KEY FEATURES Every time the tree branches, those probabilities have to add up to 100%. The probabilities at the bottom are found by multiplying the percentages along the path. The bottom percentages must all. H (0. 5) add up to 100%. H (0. 5 ) H (0. 5) T (0. 5 ) T (0. 5) H T (0. 5) T H (0. 5) T (0. 5) 0. 125 0. 125

EXAMPLE We know there are 8 total outcomes because that’s how many paths there are. H (0. 5 ) Now, we can use that to H (0. 5) calculate the probability of… T (0. 5) H (0. 5) T (0. 5 ) H (0. 5) H T (0. 5) T H (0. 5) T (0. 5) 0. 125 0. 125

EXAMPLE • H (0. 5 ) H (0. 5) T (0. 5 ) T (0. 5) H T (0. 5) T H (0. 5) T (0. 5) 0. 125 0. 125

EXAMPLE • H (0. 5 ) H (0. 5) T (0. 5 ) T (0. 5) H T (0. 5) T H (0. 5) T (0. 5) 0. 125 0. 125

EXAMPLE You flip a coin, then draw a marble from a bag. If you flip Heads, the bag has red and blue marbles. If you flip Tails, the bag has red, blue and green marbles. Draw a tree diagram. H (0. 5 ) R (0. 5) 0. 25 B (0. 5) 0. 25 T (0. 5 ) R (0. 33) 0. 166 B (0. 33) 0. 166 G (0. 33) 0. 166

EXAMPLE • H (0. 5 ) R (0. 5) 0. 25 B (0. 5) 0. 25 T (0. 5 ) R (0. 33) 0. 166 B (0. 33) 0. 166 G (0. 33) 0. 166

EXAMPLE • H (0. 5 ) R (0. 5) 0. 25 B (0. 5) 0. 25 T (0. 5 ) R (0. 33) 0. 166 B (0. 33) 0. 166 G (0. 33) 0. 166

STOP END OF 6/8 CONTINUE TOMORROW

PART 3 TREE DIAGRAMS HOMEWORK: DAY 4 HW (1, 2, 4)

WARM-UP A dice is rolled that has 3 “A” faces, 2 “B” faces, and 1 “C” face. A colored marble is then randomly drawn from the bag whose letter was rolled. Draw a tree diagram to show all the possible outcomes.

WARM-UP A (3/6) R (3/5) 9/30 B R (2/5) (4/5) 6/30 8/30 B (2/6) C (1/6) R B (1/5) (2/5) 2/30 B (3/5) 3/30

WARM-UP •

EXAMPLE 3 girls are trying out for different sports. Gladys has a 40% chance of making her team. Becky has a 30% chance of success for making her team. Serita has a 25% chance of success for making her team. Fill in the percentages for the tree diagram.

EXAMPLE 30% 70% 40% 60% 30% 70% 25% 3% 75% 25% 9% 7% 75% 21% 4. 5 % 13. 5 % 10. 5 % 75% 25% 75% 31. 5 %

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STOP END OF 6/9 START PART 4 TOMORROW