34. A carnival game has a wheel with a spinner and two colors: red and black. Spinning the wheel gives an equal probability of landing on either color. If red is the observed outcome for 4 spins of the wheel in a row, what is the probability that on the fifth spin of the wheel, red would again be the observed outcome?
Answer: B
The probability of landing on red on the fifth spin is 0.5.
Since the wheel has an equal probability of landing on either color, the outcome of previous spins does not affect the probability of the next spin. Therefore, the probability of landing on red on the fifth spin remains 0.5.
A) 0.2
This option is incorrect as it suggests a lower probability of landing on red. The game is designed with equal chances for both colors; thus, 0.2 does not reflect the true probability of landing on red.
B) 0.5
This option is correct because the probability of landing on red is consistently 0.5 for each spin of the wheel, regardless of past outcomes. The independence of each spin ensures that previous results do not influence the next one.
C) 0.8
This option is incorrect because it overestimates the probability of landing on red. Since the outcomes are independent and the wheel is fair, the probability cannot exceed 0.5 for either color.
D) 1
This option is incorrect as it implies certainty in landing on red. The wheel offers equal chances for red and black, meaning that while red could occur again, it is not guaranteed.
Conclusion
The correct answer is 0.5, reflecting the equal probability of landing on either color in a fair game. All other options fail to recognize the independence of each spin, which maintains the probability of 0.5 for both outcomes regardless of previous results.