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Two events are mutually exclusive if they both cannot occur together. For example, if you toss a coin , let A represent a head showing up and B represent a tail showing up. These two events are mutually exclusive. You can only have a tail or head.
To explain an independent event, pick a card from a deck of 52. The probability that it is a king is 4/52. If you put the card back and draw again, the probability is still 4/52. The second draw is independent of the first draw. If you draw another card without putting it back, its probability changes to 3/51. It becomes a dependent event.
In short, a mutually exclusive event is not an independent event.
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Are complementary events also mutually exclusive events?
Yes, they are. Mutually exclusive events cannot occur together. Complementary events cannot occur together either because an event and its complement are the negative of each other.
Are mutually exclusive events also complementary events?
Not necessarily. The probability of a complementary event with probability p is 1-p. Two mutually exclusive events, however, don't necessarily add up to a probability of 1. For example, the probability of drawing a King from a standard deck of cards is 1 in 13, which the complementary probability of not drawing a King is 12 in 13. The probability, however, of drawing a Heart is 1 in 4, while the probability of drawing a Club is also 1 in 4. That leaves Diamonds and Spades, which account for the remaining probability of 2 in 4.
Can a probability distribution be a mutually exclusive listing of the outcomes of an experiment which can occur by chance and the corresponding probabilities of occurrance?
Not quite. The listing must also be exhaustive: it must contain all possible outcomes.For the roll of a fair cubic die, consider the following:Prob(1) = 1/6Prob(2) = 1/6This is a mutually exclusive listing of the outcomes of the experiment and the corresponding probabilities of occurrence but it is not a probability distribution because it does not include all possible outcomes. As a result, the total of the listed probabilities is less than 1.
What does equally unlikely mean in probability?
Two events are equally unlikely if the probability that they do not happen is the same for each event. And, since the probability of an event happening and not happening must add to 1, equally unlikely events are also equally likely,
What is the probability of getting heads only once if a fair coin is tossed 3 times?
If heads comes up on the first throw (p=0.5) then tails must come up on the next two throws (each has a p= 0.5 of occurring) so 0.5 x 0.5 x 0.5 = 0.125 for this event (HTT) The second event is THT and the third event TTH each has a 0.125 probability, so 3 x 0.125 = 0.375. You can also solve this problem with the binomial distribution p = 0.5 q= 0.5, p(x=1, n= 3) = 3!/(2! 1!)(0.5)^1(0.5)^2 = 0.375 If heads comes up on the first throw (p=0.5) then tails must come up on the next two throws (each has a p= 0.5 of occurring) so 0.5 x 0.5 x 0.5 = 0.125 for this event (HTT) The second event is THT and the third event TTH each has a 0.125 probability, so 3 x 0.125 = 0.375. You can also solve this problem with the binomial distribution p = 0.5 q= 0.5, p(x=1, n= 3) = 3!/(2! 1!)(0.5)^1(0.5)^2 = 0.375
Are complementary events also mutually exclusive events?
Yes, they are. Mutually exclusive events cannot occur together. Complementary events cannot occur together either because an event and its complement are the negative of each other.
What does the expression mutually exclusive mean?
Mutually exclusive means if one thing is true the other must be false and vice versa.If A is true, B is false. If B is true, A is false.For instance,The ball was totally red.The ball was totally blue.These are mutually exclusive because the ball can only be one or the other.The ball was red.The ball was blue.These are NOT mutually exclusive because the ball could also be red AND blue.
What are two subsets of real numbers that are mutually exclusive?
Take any set; this set and its complement are mutually exclusive. Here are some examples:Negative and non-negative (i.e., positive and zero) numbersRational and irrational numbersIntegers and non-integersAlgebraic and transcendental numbersYou can also take a set and its complement from a smaller universe; these would also be mutually exclusive. For example:Even and odd numbers (only includes integers)
Term for two mutually exclusive words like death and life?
Mutually exclusive. The two events can also be exhaustive if there is no other possibility. For example, if you believe in a state of spiritual limbo, then there is a third possible outcome. In that case death and life are no longer exhaustive.
Are mutually exclusive events also complementary events?
Not necessarily. The probability of a complementary event with probability p is 1-p. Two mutually exclusive events, however, don't necessarily add up to a probability of 1. For example, the probability of drawing a King from a standard deck of cards is 1 in 13, which the complementary probability of not drawing a King is 12 in 13. The probability, however, of drawing a Heart is 1 in 4, while the probability of drawing a Club is also 1 in 4. That leaves Diamonds and Spades, which account for the remaining probability of 2 in 4.
Do Citizens who live in socialist countries are taxed at higher rates than citizens of capitalist countries?
Socialist countries are also capitalist countries. The two are not mutually exclusive.
What do you value most chastity or bliss?
Bliss, definitely. Chastity just makes people grumpy.AnswerBoth. They are not mutually exclusive. There is also evidence that chastity can indeed lead to bliss.
Where do you get Webkinz tokens?
In exclusive packages - you can get them by logging on during a holiday or other special event. Also, sometimes when you get a new pet you get tokens.
Is glass an element or a solid?
The two categories are not mutually exclusive. A glass is, by definition, an amorphous solid. It may or may not also be an element, depending on exactly what it's made of. Ordinary window or drinking-type glass is not an element but a compound.
Was Jesus's father Joseph the carpenter or Joseph the son of Jacob?
They're not mutually exclusive. In this case, in fact, both are true. It's well known that Joseph was the carpenter, but according to Matthew 1:16, Joseph was also the son of Jacob.
Is it true the the categories of application software are mutually exclusive?
No. Lots of applications are capable of doing some of the things that others can do. There are things a spreadsheet is mainly used for that it is also possible to do in a database or even in a word processor, like calculations. You use the software that is best suited to your task. You can do calculations using a word processor, but a spreadsheet is better for that. You can filter data using a spreadsheet, but a database is better for that. Because software is not mutually exclusive you can get the to work together and do different things with the same data or transfer work from one to another.
Can a probability distribution be a mutually exclusive listing of the outcomes of an experiment which can occur by chance and the corresponding probabilities of occurrance?
Not quite. The listing must also be exhaustive: it must contain all possible outcomes.For the roll of a fair cubic die, consider the following:Prob(1) = 1/6Prob(2) = 1/6This is a mutually exclusive listing of the outcomes of the experiment and the corresponding probabilities of occurrence but it is not a probability distribution because it does not include all possible outcomes. As a result, the total of the listed probabilities is less than 1.
