Question

a spinner has 4 equal-sized sections labeled a, b, c, and d. it is spun and a fair coin is tossed. what is the probability of spinning c and flipping heads?
options:
$\frac{1}{8}$
$\frac{1}{4}$
$\frac{1}{2}$
$\frac{3}{4}$

Explanation:

Step1: Find probability of spinning "C"

The spinner has 4 equal sections (A, B, C, D). So the probability of spinning "C" is the number of favorable outcomes (1, which is C) divided by total outcomes (4). So \( P(\text{spin C}) = \frac{1}{4} \).

Step2: Find probability of flipping "heads"

A fair coin has 2 outcomes (heads, tails). So the probability of flipping heads is number of favorable outcomes (1, heads) divided by total outcomes (2). So \( P(\text{flip heads}) = \frac{1}{2} \).

Step3: Find probability of both events

Since spinning the spinner and flipping the coin are independent events, we multiply their probabilities. So \( P(\text{spin C and flip heads}) = P(\text{spin C}) \times P(\text{flip heads}) = \frac{1}{4} \times \frac{1}{2} = \frac{1}{8} \).

Answer:

\(\frac{1}{8}\) (corresponding to the first option)