If all the outcomes of a sample space have the same chance of occurrence , then it is known as equally likely outcomes. It is not necessary that the outcomes are equally likely, but during an experiment we shall assume that the outcomes are equally likely outcomes in many cases.
What is an equally likely outcome?
Equally likely means that each outcome of an experiment occurs with equal probability . For example, if you toss a fair, six-sided die, each face (1,2,3,4,5,or6 1 , 2 , 3 , 4 , 5 , or 6 ) is as likely to occur as any other face. If you toss a fair coin, a Head (H ) and a Tail (T ) are equally likely to occur.
What are equally likely outcomes of an experiment?
Equally likely means that each outcome of an experiment occurs with equal probability . For example, if you toss a fair, six-sided die, each face (1,2,3,4,5,or6 1 , 2 , 3 , 4 , 5 , or 6 ) is as likely to occur as any other face. If you toss a fair coin, a Head (H ) and a Tail (T ) are equally likely to occur.
What is the difference between likely and equally likely?
Complementary Event : The opposite of an event. That is, the set of all outcomes of an experiment that are not included in an event. Equally Likely: Two or more possible outcomes of a given situation that have the same probability.
What is equally likely outcomes and not equally likely outcomes?
Equally likely implies that the all of the outcomes have the same probability of occurring and that the event is fair. If something is not equally likely, then one or more outcomes are more likely to occur than others and the event would be unfair .
How do you list all possible outcomes?
The list of all the possible outcomes is called the SAMPLE SPACE (S) . An event is any outcome or set of outcomes of a random phenomenon. An event must be present in the sample space.
What is an example of an impossible event?
Rolling a 7 on a six-sided die is an impossible event. For example: What is the probability of rolling a 7 on a six-sided die? As the number 7 never appears on a face of a six-sided die, the event is impossible. Therefore, the probability is 0.
What is an impossible event in probability?
An impossible event is an event that cannot happen. E is an impossible event if and only if P(E) = 0 . Example. In flipping a coin once, an impossible event would be getting BOTH a head AND a tail.
What are not equally likely outcomes?
When a sample space consists of outcomes that don’t have an equal chance of occurrence , then the resultant outcomes are said to be not equally likely outcomes.
What does likely mean in probability?
1 : having a high probability of occurring or being true : very probable rain is likely today.
Do the outcomes for tossing the cup appear to be equally likely?
The outcomes of an experiment are equally likely to occur when the probability of each outcome is equal . Toss the paper cup times, and record in a table the results of each toss.
What is the probability of an event assuming all outcomes are equally likely?
If outcomes are equally likely, then the probability of an event occurring is the number in the event divided by the number in the sample space . The probability of rolling a six on a single roll of a die is 1/6 because there is only 1 way to roll a six out of 6 ways it could be rolled.
How do you calculate outcomes?
Once again, the Counting Principle requires that you take the number of choices or outcomes for two independent events and multiply them together. The product of these outcomes will give you the total number of outcomes for each event. You can use the Counting Principle to find probabilities of events.
How do you find the outcome of a sample space?
All we have to do is multiply the events together to get the total number of outcomes. Using our example above, notice that flipping a coin has two possible results, and rolling a die has six possible outcomes. If we multiply them together, we get the total number of outcomes for the sample space: 2 x 6 = 12! Cool!
What is the probability of all possible outcomes?
All possible outcomes together must have probability 1 ...the sum of the probabilities for all possible outcomes must be exactly 1. All possible outcomes is another way to say sample space, so symbolically P(S) = 1. 3. The probability that an event does NOT occur is 1 minus the probability that the event DOES occur.
What is an example of impossible?
The definition of impossible is something that cannot be done, that cannot be true, or it also is something or someone who is hard to deal with. Walking to the moon is an example of something that would be described as impossible.
