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?

Rationale

The probability that red will be the observed outcome on the fifth spin is 0.5.

In a fair carnival game where the spinner has two equally likely outcomes—red and black—the probability of landing on red remains constant at 0.5 for each spin, regardless of prior outcomes. Each spin is an independent event, meaning previous results do not influence future spins.

A (0.2) YOUR ANSWER

This choice suggests a probability of 20% for landing on red, which is incorrect. Since the spinner has two colors that are equally likely, the probability for each color must be 50%, not 20%. Therefore, this option does not reflect the fair nature of the game.

B (0.5) CORRECT

This is the correct choice, as the probability of landing on red for each spin of the wheel is consistently 0.5. Each spin is independent, meaning the outcome of the previous spins does not affect the probability of the fifth spin.

C (0.8) YOUR ANSWER

Selecting 0.8 implies an 80% chance of the next spin landing on red, which is not accurate in this scenario. The game specifies equal probabilities for red and black; thus, 0.8 does not align with the independent and fair structure of the game.

D (1) YOUR ANSWER

A probability of 1 indicates certainty that the next outcome will be red, which is not valid in this case. While red has been observed in the previous spins, the independence of each spin means that there remains a 50% chance of landing on either color, making this choice incorrect.

Conclusion

In this carnival game, the probability of landing on red for any spin of the wheel is always 0.5, irrespective of the outcomes of previous spins. The independence of each event ensures that past results do not affect future probabilities, solidifying the 50% likelihood for red on the fifth spin. This fundamental concept of independent events is crucial in understanding probability in games of chance.

The probability that red will be the observed outcome on the fifth spin is 0.5.

Related Questions

Related Quizzes

How familiar were you with this question?

Report an Issue

Rate this Practice Test