Proportionality>Representing Sample Spaces with Lists and Tree Diagrams(TEKS.Math.7.6.A)
Help Questions
Texas 7th Grade Math › Proportionality>Representing Sample Spaces with Lists and Tree Diagrams(TEKS.Math.7.6.A)
A number cube labeled 1–6 is rolled, then a coin is flipped. Write outcomes as (number, coin). Which list shows all outcomes?
(1,H), (1,T), (2,H), (2,T), (3,H), (3,T), (4,H), (5,H), (5,T), (6,H)
(1,H), (1,T), (2,H), (2,T), (3,H), (3,T), (4,H), (4,T), (5,H), (5,T), (6,H), (6,T)
(H,1), (T,1), (H,2), (T,2), (H,3), (T,3), (H,4), (T,4), (H,5), (T,5), (H,6), (T,6)
(1,H), (1,T), (2,H), (2,T), (3,H), (3,T), (4,H), (4,T), (5,H), (5,T), (6,H), (6,H)
Explanation
There are 6 numbers and 2 coin results, so $6 \times 2 = 12$ outcomes. List systematically by number: for each 1–6, pair with H and T to get all 12: (1,H), (1,T), …, (6,H), (6,T).
A spinner has 3 equal sections labeled A, B, C. It is spun, then a 4-sided die labeled 1–4 is rolled. How many outcomes are in the sample space? (Write outcomes as (letter, number).)
1/6
1/7
1/11
1/23
Explanation
There are 3 spinner results and 4 die results, so $3 \times 4 = 12$ outcomes. A systematic list would be (A,1)–(A,4), (B,1)–(B,4), (C,1)–(C,4).
To order a smoothie, first choose a size (small, large), then choose one fruit (strawberry, mango, banana). Write outcomes as (size, fruit). Which list shows all outcomes?
(small, strawberry), (small, mango), (large, strawberry), (large, mango), (large, banana)
(small, strawberry), (small, mango), (small, mango), (small, banana), (large, strawberry), (large, mango)
(strawberry, small), (mango, small), (banana, small), (strawberry, large), (mango, large), (banana, large)
(small, strawberry), (small, mango), (small, banana), (large, strawberry), (large, mango), (large, banana)
Explanation
There are 2 sizes and 3 fruits, so $2 \times 3 = 6$ outcomes. Listing by size: all small with each fruit, then all large with each fruit gives the 6 pairs shown.
Two coins are flipped in order (coin 1, then coin 2). How many outcomes are in the sample space?
1/3
1/2
1/1
1/5
Explanation
Each flip has 2 outcomes, so $2 \times 2 = 4$. The outcomes are (H,H), (H,T), (T,H), (T,T).
A bag has one red (R), one blue (B), and one green (G) marble. You draw one marble, replace it, then draw again. Write outcomes as (first draw, second draw). Which list shows all outcomes?
(R,R), (R,B), (R,G), (B,R), (B,B), (G,R), (G,G)
(R,B), (B,R), (R,G), (G,R), (B,G), (G,B)
(R,R), (R,B), (R,G), (B,R), (B,B), (B,G), (G,R), (G,B), (G,G)
(R,R), (R,B), (R,G), (B,R), (B,B), (B,G), (G,R), (G,B), (G,G), (R,R)
Explanation
With replacement, there are 3 choices each time, so $3 \times 3 = 9$ outcomes. List all ordered pairs: (R,R), (R,B), (R,G), (B,R), (B,B), (B,G), (G,R), (G,B), (G,G).