The probability of an event is the likelihood of that event occuring. Probability is a value between (and including) zero and one. Show
If P(E) represents the probability of an event E, then 0 ≤ P(E) ≤ 1. An experimental probability is measured. A theoretical probability is calculated. An event with a probability of zero [P(E) = 0] will never occur (an impossible event). An event with a probability of one [P(E) = 1] means the event must occur (a certain event). An event with a probability of 0.5 [P(E) = 0.5] is sometimes called a fifty-fifty chance event or an even chance event. An event with a higher probability is more likely to occur than one with a lower probability. The correct option is B0Explanation for correct option:The probability of an impossible event is PφThe probability of an event which is not possible is always 0 Therefore Pφ=0.For instance, If we roll a fair die, the possibility is that you will get a number not more than 6. There is a possibility of getting outcome 1,2,3 ,4,5or 6. Here, outcome 9 or any number greater than 6 is an impossible outcome, not included in sample space. Thus, we can conclude that the probability of an impossible event is 0.The likelihood that an event won't happen at all or that it won't have any chance of happening in the future is known as the probability of an impossible occurrence.Therefore theprobability of impossible event that is Pφ=0 Hence, option (B) is correctQ. Fill in the blanks: (i) Probability of a sure event is ............... (ii) Probability of an impossible event is ................ (iii) The probability of an event (other than sure and impossible event) lies between ................. (iv) Every elementary event associated to a random experiment has .............. probability. (v) Probability of an event A + Probability of event 'not A' = ................ (vi) Sum of the probabilities of each outcome in an experiment is ................ Probability > The probability of an impossible event is 0. Impossible events can’t occur. 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. A certain event is just the opposite: it will happen under every circumstance. For example, if a six-sided die has the number 3 on all faces, then the probability of the event “rolling a 3” is 1. Although the probability of an impossible event is zero, it doesn’t mean that
every event with zero probability is impossible. There are many situations where an event doesn’t happen under some circumstances (i.e. it has a probability of zero for a certain model or situation) but it can happen in others. Here’s a straightforward example: Given that a classroom contains all boys, what is the probability of choosing a girl at random? The probability is 0, as it’s impossible to choose a girl if the classroom only has boys. However, that doesn’t mean the event of choosing a girl is impossible: change the situation slightly (by adding girls to the classroom), and the probability changes. Probability of an Impossible Event = Empty SetAn impossible event is equal to the empty set ∅. This is a rule of probability, which can formally be written as [1]: The impossible event, defined in this way as a set with no elements, doesn’t correspond to any experimental result, but it is useful in some calculations [2]. References[1] Probability: Key Definitions. Retrieved June 11, 2020 from: https://www.regent.edu/app/uploads/2018/06/ML-Math-101-Probability.pdf” rel=”noopener” target=”_blank”>Probability: Key Definitions. Retrieved June 11, 2020 from: https://www.regent.edu/app/uploads/2018/06/ML-Math-101-Probability.pdf ---------------------------------------------------------------------------
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If it is impossible that an event will occur the probability of it happening is
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