In a game, a coin is tossed, and a spinner with 8 equal spaces numbered 1 through 8 is spun. What is the probability of getting heads on the coin and a number less than 3 on the spinner?
The probability of getting heads on the coin and a number less than 3 on the spinner is 1/4.
To find the combined probability of independent events, we multiply the probabilities of each event occurring. The probability of getting heads on the coin is 1/2, and the probability of spinning a number less than 3 on an 8-space spinner (which includes the numbers 1 and 2) is 2/8 or 1/4. Therefore, the overall probability is (1/2) * (1/4) = 1/8.
While 1/8 is the product of the individual probabilities, it misrepresents the specific combination of outcomes being asked for in the question. The probability of getting heads (1/2) and a number less than 3 (1/4) combines to yield a different result, emphasizing the need to accurately calculate the product of the two probabilities.
This choice mistakenly presents the probability of spinning a number less than 3 alone, which is indeed correct as it represents the likelihood of that single event. However, it fails to account for the outcome of the coin toss, leading to an incomplete answer regarding the combined event's probability.
This option reflects the probability of getting heads on the coin toss alone and does not consider the spinner's outcome at all. It suggests that only the coin's result is relevant, which disregards the essential component of the spinner's contribution to the overall probability calculation.
This choice incorrectly assumes a combined probability involving more outcomes than intended. It may stem from a misunderstanding of how to apply the multiplication rule for independent events, leading to an inflated probability that does not align with the specific scenario presented in the question.
The correct calculation for the probability of getting heads on the coin and a number less than 3 on the spinner combines the probabilities of two independent events. The resulting probability of 1/4 accurately represents this scenario, while the other options incorrectly interpret the relationship between the coin toss and the spinner outcomes. Understanding how to multiply probabilities of independent events is crucial for accurate probability assessments in games and other applications.
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