Question

1. a model says that a spinning coin falls heads up with a probability of 0.5. would a result of 6 tails in a row cause you to question the model? why or why not?

Explanation:

Step1: Calculate probability of 6 - tails in a row

The probability of getting tails in a single fair - coin spin is \(p = 0.5\). Since the spins are independent events, the probability of getting 6 tails in a row is \(P=(0.5)^6\).

$$P=(0.5)^6=\frac{1}{2^6}=\frac{1}{64} = 0.015625$$

Step2: Analyze the result

A probability of \(0.015625\) (or \(1.5625\%\)) is a relatively low - probability event. However, low - probability events can still occur in a random process. Just because an event with a low probability has occurred does not necessarily mean the model is wrong.

Answer:

No, a result of 6 tails in a row would not necessarily cause you to question the model. Although the probability of getting 6 tails in a row is low (\(0.015625\)), low - probability events can occur in random processes.