Question

independent practice
for each situation, determine the sample space. use a list or tree
diagram. (examples 1–2)

1. tossing a coin and spinning

the spinner at the right

1. picking a number from 1 to 5 and choosing

the color red, white, or blue

1. choosing a purple, green, black, or silver bike

having 10, 18, 21, or 24 speeds

1. choosing a letter from the word space and

choosing a consonant from the word math

Explanation:

Problem 1: Tossing a coin and spinning the spinner

Step 1: Determine coin outcomes

A coin has 2 outcomes: Heads (H) and Tails (T).

Step 2: Determine spinner outcomes

The spinner has 5 outcomes: 1, 2, 3, 4, 5.

Step 3: List all combined outcomes

For each coin outcome, pair with each spinner outcome:

• Heads: (H,1), (H,2), (H,3), (H,4), (H,5)
• Tails: (T,1), (T,2), (T,3), (T,4), (T,5)

Sample space = {(H,1), (H,2), (H,3), (H,4), (H,5), (T,1), (T,2), (T,3), (T,4), (T,5)}

Step 1: Determine number outcomes

Numbers: 1, 2, 3, 4, 5 (5 outcomes).

Step 2: Determine color outcomes

Colors: red (R), white (W), blue (B) (3 outcomes).

Step 3: List all combined outcomes

Pair each number with each color:
(1,R), (1,W), (1,B),
(2,R), (2,W), (2,B),
(3,R), (3,W), (3,B),
(4,R), (4,W), (4,B),
(5,R), (5,W), (5,B)
Sample space = \{(1,R), (1,W), (1,B), (2,R), (2,W), (2,B), (3,R), (3,W), (3,B), (4,R), (4,W), (4,B), (5,R), (5,W), (5,B)\}

Step 1: Determine color outcomes

Colors: purple (P), green (G), black (Bl), silver (S) (4 outcomes).

Step 2: Determine speed outcomes

Speeds: 10, 18, 21, 24 (4 outcomes).

Step 3: List all combined outcomes

Pair each color with each speed:
(P,10), (P,18), (P,21), (P,24),
(G,10), (G,18), (G,21), (G,24),
(Bl,10), (Bl,18), (Bl,21), (Bl,24),
(S,10), (S,18), (S,21), (S,24)
Sample space = \{(P,10), (P,18), (P,21), (P,24), (G,10), (G,18), (G,21), (G,24), (Bl,10), (Bl,18), (Bl,21), (Bl,24), (S,10), (S,18), (S,21), (S,24)\}

Answer:

Sample space: \(\{(H,1), (H,2), (H,3), (H,4), (H,5), (T,1), (T,2), (T,3), (T,4), (T,5)\}\)

Problem 2: Picking a number (1–5) and choosing a color (red, white, blue)