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 of landing on red on the fifth spin is 0.5.

The outcome of each spin of the wheel is independent of previous spins, meaning that the results of the earlier spins do not influence the outcome of the next spin. Since the wheel has an equal probability of landing on either color, the chance of landing on red for any single spin remains constant at 0.5.

A (0.2) YOUR ANSWER

A probability of 0.2 suggests that there is a 20% chance of landing on red. However, since the wheel is designed with equal probabilities for red and black, this value misrepresents the actual likelihood of the outcome.

B (0.5) CORRECT

This choice correctly reflects the equal probability of the spinner landing on red or black in each independent spin. Each spin has a 50% chance of resulting in red, regardless of previous outcomes, making this the accurate probability.

C (0.8) YOUR ANSWER

A probability of 0.8 implies an 80% chance of landing on red. Given that the game setup specifies an equal likelihood for both colors, this value overestimates the probability and incorrectly assumes a skewed distribution.

D (1) YOUR ANSWER

A probability of 1 indicates that landing on red is a certainty. This is incorrect because the game allows for the possibility of landing on black, meaning the outcome is not guaranteed to be red.

Conclusion

In independent probability events, previous outcomes do not affect future results. The probability of landing on red remains consistently at 0.5 for each spin of the wheel, regardless of the outcomes of prior spins. Understanding this principle is crucial for accurately assessing probabilities in games of chance.

The probability of landing on red 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