Question

1. what is the probability of tossing a number - cube labeled 1 - 6 and spinning the spinner shown and getting a sum of 9 or greater? a. $\frac{1}{6}$ b. $\frac{5}{24}$ c. $\frac{1}{4}$ d. $\frac{3}{8}$

Explanation:

Step1: Find total number of outcomes

The die has 6 outcomes and the spinner has 4 outcomes. By the fundamental counting principle, the total number of combined outcomes is $6\times4 = 24$.

Step2: List pairs with sum of 9 or greater

List all pairs of die - spinner results and their sums:

• Die = 1: Sums with spinner values (1 + 2 = 3, 1+3 = 4, 1 + 4 = 5, 1+5 = 6)
• Die = 2: Sums (2 + 2 = 4, 2+3 = 5, 2 + 4 = 6, 2+5 = 7)
• Die = 3: Sums (3 + 2 = 5, 3+3 = 6, 3 + 4 = 7, 3+5 = 8)
• Die = 4: Sums (4 + 2 = 6, 4+3 = 7, 4 + 4 = 8, 4+5 = 9)
• Die = 5: Sums (5 + 2 = 7, 5+3 = 8, 5 + 4 = 9, 5+5 = 10)
• Die = 6: Sums (6 + 2 = 8, 6+3 = 9, 6 + 4 = 10, 6+5 = 11)

The pairs with sum 9 or greater are (4,5), (5,4), (5,5), (6,3), (6,4), (6,5), so there are 6 such pairs.

Step3: Calculate probability

The probability $P$ is the number of favorable outcomes divided by the total number of outcomes. So $P=\frac{6}{24}=\frac{1}{4}$.

Answer:

C. $\frac{1}{4}$