# i put 3 question answer each q different

(1)

Get 4 coins. You are interested in the number of heads that shows when you flip 4 coins.

Find the Empirical Probability P(getting a total of exactly 3 heads), by tossing these 4 coins a total of 30 times and keeping track of the number of heads of each 4-coin toss.

Reply to this post with the following information:

1. The empirical probability of getting exactly 3 heads, as a fraction.
2. The same probability as a percentage.
3. The theoretical probability of getting exactly 3 heads when tossing 4 coins (hint: use the Counting Principle to figure out the total number of outcomes when tossing 4 coins, for the bottom of your probability fraction. For the top, find the number of outcomes with exactly 3 heads by listing out those outcomes. It might help to realize that this is the same as having exactly one tail).

(2)

Get 3 coins: a penny, a nickel, and a dime. When you flip all three at once, you are going to count the value of a coin only if it lands heads up. So for example, if you flip the three coins and the penny and dime show heads, but the nickel shows tails, then you would count the total as 1 + 10 = 11 cents.

Find the Empirical Probability P(getting a total of 10 or more cents), by tossing these 3 coins a total of 30 times and keeping track of the total of each 3-coin toss.

Reply to this post with the following information:

1. The empirical probability of getting a total of 10 or more cents, as a fraction.
2. The same probability as a percentage.
3. The theoretical probability of getting a total of 10 or more cents (hint: look at the list of outcomes of a 3-coin toss from our lecture slides and replace each H with the coin value, and each T with a 0. Then total up the number of cents in each outcome and count the number of outcomes that are 10 or higher for the numerator in your probability fraction).

(3)

Get a pair of dice. If you don’t have any dice, you can use a dice-rolling simulator such as this one: Pair of Dice Simulator. You are interested in the probability of getting a sum or 4 or less.

Find the Empirical Probability P(getting a sum or 4 or less), by tossing this pair of dice a total of 30 times and keeping track of the sum of each 2-dice toss.

Reply to this post with the following information:

1. The empirical probability of getting a sum of 4 or less, as a fraction.
2. The same probability as a percentage.
3. The theoretical probability of getting a sum of 4 or less (hint: use the Counting Principle to figure out the total number of outcomes when tossing a pair of dice – we covered this in class – for the bottom of your probability fraction. For the top, find the number of outcomes with a sum of 4 or less by listing out those outcomes).

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