Assume that a coin is tossed twice. The coin may not be fair. The sample space consists of the outcomes {HH, HT, TH, TT}.

Question

Probability- HH: 0.33
HT: 0.21
TH: 0.49
TT: -0.97

Is the given a probability model?

Answer 1

To determine if the given data represents a valid probability model, we need to check two conditions:

1. Each probability must be between 0 and 1 (inclusive).
2. The sum of all probabilities must equal 1.

Given probabilities:

• P(HH) = 0.33
• P(HT) = 0.21
• P(TH) = 0.49
• P(TT) = -0.97

Let's check the first condition:

• P(HH) = 0.33 (valid, as it's between 0 and 1)
• P(HT) = 0.21 (valid)
• P(TH) = 0.49 (valid)
• P(TT) = -0.97 (invalid, as it's less than 0)

Now, let's check the second condition by summing the probabilities:

\[ P(HH) + P(HT) + P(TH) + P(TT) = 0.33 + 0.21 + 0.49 - 0.97 = 0.06 \]

The total sum is 0.06, which is not equal to 1.

Since one of the probabilities is negative and the total sum of probabilities does not equal 1, the given data does not represent a valid probability model.