Hi I need help with my statistics homework for probability. The question is, Dis
ID: 3200241 • Letter: H
Question
Hi I need help with my statistics homework for probability. The question is, Discuss complementary events (and the "rule of complementary events"), a compound event, the addition rule of probability, disjoint events, the multiplication rule of probability, and independent events? I need help explaining what they are for a paper and then I have to discuss them in class. I look in my textbook but it doesn't explain it in a clear way. I would really appreciate if there is a better way to explain these terms and with the help of examples. Thank you!
Explanation / Answer
Complementary events (and the "rule of complementary events"), -
Rule: Sum of probability of complmentry events is 1
Example: The probability of getting a head is complementry to probability of getting a tail. If you add up the 2 probabilite you will get a 1. So, P( head)= 1/2, P( tail) = 1/2, add them up you will get 1
A compound event - An event that consists of 2 or more events.
Lets defined our compund event as probability of getting a head or a tail: thats' 1/2+1/2 = 1
The addition rule of probability - When two events, A and B, are mutually exclusive, the probability that A or B will occur is the sum of the probability of each event. Here in out example, since the probability of tail doesn't overlap with probability of getting head , we can add up. Getting A and B events are mutually exclusive.
Disjoint events - Another word that means mutually exclusive is disjoint. If twoevents are disjoint, then the probability of them both occurring at the same time is 0. So in other terms , probability of getting a head and tail both are not possible and therefore mutually exlsuive, or disjoint.
The multiplication rule of probability - The multiplication rule also deals with two events, but in these problems the events occur as a result of more than one task (rolling one die then another, drawing two cards, spinning a spinner twice, pulling two marbles out of a bag, etc).
Lets take our example - Whats' probability of getting 2 heads in 2 tosses of coins: So, P( head) = 1/2
2 head's = P(head)*P(head) = 1/2 * 1/2 = 1/4
Independent events Two events, A and B, are independent if the fact that A occurs does not affect the probability of B occurring. For example, Landing on heads after tossing a coin AND rolling a 5 on a single 6-sided die are independent events. One is not dependent on the other.