Vocab
__?__ events, or __?__ __?__ events are events that have no outcomes in common.
__?__ events are events that have one or more outcomes in common.
For two __?__ events, the probability that either of the events occurs is the sum of the probabilities of the events.
For two __?__ events, the probability that either of the events occurs is the sum of the probabilities of the events minus the probability of both events.
Two events are __?__ events if they are disjoint events and one event or the other must occur.
What are your choices? What are your answers?
I have no choices lol and I only answered the first two
I'm sure the words and the definitions are in your text.
What are your answers for the first two?
1. Disjoint, mutually exclusive
2 overlapping
Those answers are correct.
You also may find some answers in this site.
http://quizlet.com/18751599/probability-vocabulary-flash-cards/
Vocab:
1. Mutually exclusive events, or disjoint events, are events that have no outcomes in common.
2. Dependent events are events that have one or more outcomes in common.
3. For two mutually exclusive events, the probability that either of the events occurs is the sum of the probabilities of the events.
4. For two dependent events, the probability that either of the events occurs is the sum of the probabilities of the events minus the probability of both events.
5. Two events are complementary events if they are disjoint events and one event or the other must occur.
To understand these concepts, it may be helpful to consider examples and use probability notation.
For example, let's say we have a bag of colored marbles: 5 red marbles and 3 blue marbles.
1. Mutually exclusive events: If we define event A as drawing a red marble and event B as drawing a blue marble, these events have no outcomes in common. Therefore, they are mutually exclusive or disjoint events.
2. Dependent events: Now, let's define event C as drawing a red marble in the first draw and event D as drawing a red marble in the second draw, both without replacement. These events have one outcome in common, which is drawing a red marble. Therefore, they are dependent events.
3. Calculating probabilities for mutually exclusive events: If we want to know the probability of drawing either a red or a blue marble from the bag, we can calculate the probability of event A (drawing a red marble) and the probability of event B (drawing a blue marble) and add them together. In this case, P(A) = 5/8 (since there are 5 red marbles out of 8 total marbles) and P(B) = 3/8. So, P(A or B) = P(A) + P(B) = 5/8 + 3/8 = 8/8 = 1.
4. Calculating probabilities for dependent events: Continuing with events C and D, if we want to know the probability of drawing a red marble in either the first or second draw, we calculate the probability of event C and the probability of event D and subtract the probability of both events occurring (drawing a red marble in both draws). In this case, P(C) = 5/8 (as above) and P(D) = 4/7 (since there is one less red marble after the first draw). The probability of both events occurring is P(C and D) = (5/8) * (4/7) = 20/56. So, P(C or D) = P(C) + P(D) - P(C and D) = 5/8 + 4/7 - 20/56 = 35/56 ≈ 0.625.
5. Complementary events: Lastly, complementary events refer to two disjoint events where one event or the other must occur. For example, if we define event E as drawing a red marble and event F as drawing a blue marble, these events are mutually exclusive. If we know that a marble must be drawn from the bag, then either event E or event F must occur.
Understanding and applying these concepts allows us to analyze different types of events and calculate their probabilities using basic arithmetic operations.