Addition Rule
The addition rule is a fundamental concept in probability theory, essential for calculating the probability of the union of two or more events. It states that the probability of the union of two events A and B is equal to the sum of their individual probabilities minus the probability of their intersection. This principle allows for the calculation of probabilities in scenarios where events are not mutually exclusive, providing a foundational tool for analyzing and predicting outcomes in various fields such as statistics, economics, and engineering.
Questions
- Two dice are thrown. Event #A# is "the sum of two dice is #7#" and Event #B# is "at least one die is #6#". Are #A# and #B# independent?
- Suppose you are playing a game in which two fair dice are to rolled. To make the first move, you need to roll doubles or a sum of 3 or 11. What is the probability that you will be able make the first move?
- A set of cards has 5 red cards and 5 black cards. If 3 cards are selected at random, what is the probability to select at least 1 black card?
- There were five people in group A, with a mean lQ of 100, and five in group B, with a mean IQ of 74. When Jack left group A for group B, both means increased, and the total of the two new means was 180. What Is Jack's IQ?
- Jonathan's math test scores were 87, 93, 85, 62, and 95. What was his mean score?
- Could we use the special addition rule for determining the probability that for one draw from a deck of cards, that the card is either a Queen or a Heart? Why or why not?
- What is another name for mutually exclusive events?
- What is the probability that, in a single draw from a standard deck of cards, we will get either a Jack or a Diamond?
- Kevin is rolling two dice together and adding them up. Which sums should come up the most frequently?
- What is the probability of flipping a coin and getting a heads, given that the probability of getting a tails is the same, and there is no chance that the coin lands on its side?
- Two dice are rolled, what is the probability that their sum will be less than 13?
- When do you add probabilities?
- If two dice are rolled, what is the probability that the sum of the dice is 10?
- The average of three numbers is #5#. If the sum of two of the numbers is #6#, what is the third number?
- What is the average of 27 and 45?
- Two fair dice are thrown.How do you find the probability that the sum of the numbers thrown is not less than 6 ?
- In a statistics class there are 11 juniors and 6 seniors; 4 of the seniors are females, 6 of the juniors are males. If a student is selected at random, what is the probability that the student is either a senior or a male?
- There is 16 white, 9 red and 7 yellow tulips. What's the probability of randomly picking 9 flowers where 2 are white, 3 are red, and 4 are yellow?
- The probability that John falls off a ladder and breaks his arm is 0.2, and the probability that John falls off a ladder and breaks his leg is .08. Are these events mutually exclusive (disjoint)? Why or why not?
- Could someone explain to me the Rule of Compound Probability involving "and"?