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If the probability that an event will occur is three eighths then what is the probability that the event will not occur on the first trial and not occur on the second trial?
This question does not have a unique answer unless we make an additional assumption: we must know something about the relationship between the trials. For example, if we are monitoring a lightbulb for failure and the "event" consists of a working lightbulb, then the event not occurring means the lightbulb doesn't work. Let the "trials" consist of turning on the lightbulb. If the bulb fails on the first trial (chance of 1 - 3/8 = 5/8) then obviously it will not work on the second trial, either. The answer in this case would be 5/8 = 62.5%. If we assume the two trials are statistically independent, we are really saying we don't want to worry about these issues. Equivalently, the person asking the question is just telling us to multiply the probabilities (which means they are probably a teacher or a textbook and they or it are mainly concerned about your ability to multiply fractions, not about your understanding of probability). The chances of the event not occurring in each trial are 5/8. Multiplying gives 25/64 = about 39%. This is quite a bit less than 62.5%.
Does the probability of failure vary from trial to trial under binomial distribution?
No. It must remain the same.
If two events are mutually exclusive what is the probability that both occur at the same time?
The probability is 0. Consider the event of tossing a coin . The possible events are occurrence of head and tail. they are mutually exclusive events. Hence the probability of getting both the head and tail in a single trial is 0.
The chance that a given event will occur usually expressed between the number 0 will not occur and 1 the event will occur is called?
The chance that a given event will occur, usually expressed between the number 0 (will not occur) and 1 (will occur) is called probability.
Does Probability predict what will definitely occur?
The laws of probability predict what is likely to occur, not necessarily what will occur.
