I am having a difficult time understanding theProbability Distribution.

1. A probability distribution indicates the probability of all possible events in a population.We devise it based on the expected relative frequency of each event in the population.

Flip a coin 30 times and document the result of each toss. Then provide both the empirical and theoretical probability distributions.Use the appropriate expression for probability.

Empirical probability distribution

Theoretical Probability Distribution

2. What is the theoretical probability of flipping a coin 5 times and getting heads every time?

3. What is the theoretical probability of flipping a coin 7 times and getting tails every time?

Formula: p=1/2^7

Formula for #2 and #3:

P= number of favorable cases/number of possible outcomes

For help with thinking about this formula consider the following:

When you toss a coin one time, what is the probability of getting a heads?

The number of favorable cases = 1 (getting heads)

The number of possible outcomes = 2 (there are two outcomes, heads and tail)

P(probability of getting head in one toss) = 1/2 or 50%

What about when you toss a coin two times? What is the probability of getting heads both times?

The number of favorable cases = 1 (getting a heads both times)

The number of possible outcomes = 2X2 or 2^2 (4 possible outcomes which would be: Heads/Heads, Heads/Tails, Tails/Heads, Tails/Tails)

P(probability of getting 2 heads in both coin tosses) = 1/4 or .25 or 25%

What about when you toss a coin three times? What is the probability of getting heads both times

The number of favorable cases = 1 (getting a heads all three times)

The number of possible cases = 2X2x2 or 2^3 (8 possible outcomes)

P(probability of getting 3 heads in all three coin tosses) = 1/8 or .125 or 13%