a spinner has 4 equal - sized sections labeled a, b, c, and d. it is spun and a fair coin is tossed. what is…

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\?\n\\(\\frac{1}{8}\\)\n\\(\\frac{1}{4}\\)\n\\(\\frac{1}{2}\\)\n\\(\\frac{3}{4}\\)

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\?\n\\(\\frac{1}{8}\\)\n\\(\\frac{1}{4}\\)\n\\(\\frac{1}{2}\\)\n\\(\\frac{3}{4}\\)

Answer

Explanation:

Step1: Calculate probability of spinning "C"

The spinner has 4 equal - sized sections. The probability of spinning "C" is $P(C)=\frac{1}{4}$ since there is 1 "C" out of 4 sections.

Step2: Calculate probability of flipping "heads"

A fair coin has 2 possible outcomes (heads or tails). The probability of flipping "heads" is $P(H)=\frac{1}{2}$.

Step3: Use multiplication rule for independent events

Since spinning the spinner and flipping the coin are independent events, the probability of both events occurring is $P = P(C)\times P(H)$. Substitute the values: $P=\frac{1}{4}\times\frac{1}{2}=\frac{1}{8}$.

Answer:

$\frac{1}{8}$