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"?
Answer (2)
The probability of spinning 'C' on the spinner is 4 1 and the probability of flipping 'heads' on a coin is 2 1 . By multiplying these probabilities, the final answer shows that the probability of both events occurring together is 8 1 .
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Probability of spinning 'C': 4 1 .
Probability of flipping 'heads': 2 1 .
Multiply the probabilities since the events are independent: 4 1 × 2 1 .
The probability of both events occurring is: 8 1 .
Explanation
Problem Introduction Let's break down this probability problem step by step!
Probability of Spinning 'C' First, we need to determine the probability of spinning a 'C' on the spinner. Since the spinner has 4 equal-sized sections (A, B, C, and D), the probability of landing on any one of them, including 'C', is 4 1 .
Probability of Flipping 'Heads' Next, we need to find the probability of flipping 'heads' on a fair coin. A fair coin has two sides, 'heads' and 'tails', so the probability of flipping 'heads' is 2 1 .
Combined Probability Calculation Since spinning the spinner and flipping the coin are independent events, we can find the probability of both events happening by multiplying their individual probabilities: P ( " C " and heads ) = P ( " C " ) × P ( heads ) = 4 1 × 2 1 Multiplying these fractions gives us: 4 1 × 2 1 = 8 1 So, the probability of spinning 'C' and flipping 'heads' is 8 1 .
Final Answer Therefore, the probability of spinning "C" and flipping "heads" is 8 1 .
Examples
Imagine you're designing a simple game. To win, a player needs to spin a specific section on a spinner and flip a coin to land on heads. Knowing the probability of these independent events occurring together helps you balance the game's difficulty and fairness, ensuring it's neither too easy nor too hard to win.
