Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 24.4 Tree Diagrams to secure good marks & knowledge in the exams.
McGraw-Hill Math Grade 8 Answer Key Lesson 24.4 Tree Diagrams
Exercises
DIAGRAM
Question 1.
Phil first rolls a 6-sided number cube then flips a coin. Draw a tree diagram that shows all the possible outcomes. How many different outcomes are there? How many outcomes exist where Phil rolls an even number and he flips a coin “heads”?
Answer:
Total different outcomes = 12.
The coin is fair, the probabilities of getting a head and a tail are equal = 12Â .
The probability of getting an even number on a die is 36 = 12 (because among 6 results there are 3 even numbers)
Explanation:
Phil first rolls a 6-sided number cube then flips a coin.
Number of outcomes of a cube Phil first rolls = 6.
Number of outcomes of a coin Phil second rolls = 2.
Total different outcomes = Number of outcomes of a cube Phil first rolls × Number of outcomes of a coin Phil second rolls
= 6 × 2
= 12.
The coin is fair, the probabilities of getting a head and a tail are equal = 12Â .
The probability of getting an even number on a die is 36 = 12 (because among 6 results there are 3 even numbers)
.Question 2.
Felicia is laying out her wardrobe for an upcoming vacation. She will be gone 4 days. She lays out 4 shirts (blue, black, red, yellow), 3 pairs of pants (black, tan, white), and 3 pairs of shoes (black, brown, red). Draw a tree diagram to show all of the different combinations of outfits that Felicia could wear on the trip. How many combinations are there? ______________
If Felicia brings only two pairs of shoes but adds another shirt, how many possible combinations will she have? ________________
Answer:
Total outcomes of combinations she have = 40.
Explanation:
Number of days she will be gone = 4 .
Number of shirts she lays out = 4 (blue, black, red, yellow)
Number of pairs of pants = 3 (black, tan, white)
Number of pairs of shoes = 3 (black, brown, red).
Outcomes of wearing shirts = 4 × 4 = 16.
Outcomes of wearing pants = 4 × 3 = 12.
Outcomes of wearing shoes = 4 × 3 = 12.
Total outcomes of combinations she have = Outcomes of wearing shirts + Outcomes of wearing pants + Outcomes of wearing shoes
= 16 + 12 + 12
= 28 + 12
= 40.
If Felicia brings only two pairs of shoes but adds another shirt, how many possible combinations will she have?
Number of shoes she has = 2.
Number of shirts she has = 5.
Outcomes of wearing shirts = 4 × 5 = 20.
Outcomes of wearing pants = 4 × 3 = 12.
Outcomes of wearing shoes = 4 × 2 = 8.
Total outcomes of combinations she have = Outcomes of wearing shirts + Outcomes of wearing pants + Outcomes of wearing shoes
= 20 + 12 + 8
= 32 + 8
= 40.