To solve this, let's first analyze the question and the data given:

1. Goal: Find the probability that the outcome is a prime number.
2. Prime Numbers on a Six-Sided Dice: Prime numbers between 1 and 6 are 2, 3, and 5.
3. Table Information:
   • Outcome 1 has a probability of 0.2.
   • Outcome 2 has a probability of 0.06.
   • Outcome 3 has a probability of 0.28.
   • Outcome 4 has a probability of 0.12.
   • Outcome 6 has a probability of 0.16.
   • Probability for Outcome 5 is missing.

Step 1: Calculate Missing Probability for Outcome 5

Since the total probability for all outcomes must add up to 1, we can set up an equation to find the missing probability for outcome 5.

$0.2 + 0.06 + 0.28 + 0.12 + P(5) + 0.16 = 1$

Solving for $P(5)$:

$P(5) = 1 - (0.2 + 0.06 + 0.28 + 0.12 + 0.16) = 1 - 0.82 = 0.18$

So, the probability for outcome 5 is $0.18$.

Step 2: Calculate the Probability of a Prime Outcome

Now, add up the probabilities of the prime outcomes (2, 3, and 5):

$P(\text{prime}) = P(2) + P(3) + P(5) = 0.06 + 0.28 + 0.18 = 0.52$

Answer

The probability that the outcome is a prime number is 0.52.

Would you like further details, or have any questions?

Here are 5 related questions for further exploration:

1. How would this probability change if we used a fair die?
2. What are some other examples of biased probability distributions?
3. How do you calculate probabilities for multiple independent dice rolls?
4. How can you verify if a given die is biased or fair?
5. How would you represent this problem in terms of probability mass functions?

Tip: When working with probabilities, always ensure that the total probability across all outcomes adds up to 1 for a complete and accurate distribution.