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Consecutive Events Consecutive Events In mathematics probability is called uncertainty of two events. Probability is used for calculation of number of chances of a specific event. For example outcomes of a coin toss can be either heads or tails (in this situation if we assume that coin falls flat on ground). Let us discuss what the probability of getting heads or tails is. We can say probability of heads is .5 and probability of tails is .5 and thus total probability is 1. An event of probability 0 implies that is not possible. We can express the probability in mathematical form. The total number of possibilities of a particular outcome divided by total number of events is: Probability measures chance, such as when an event might occur. For example, the probability that you get a specific card out of a deck of cards equals 1 in 52, because there are 52 cards per deck. However, when you have multiple events, you need to know the probabilities of both and then multiply the two probabilities to find the probability they both occur.

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p(a) = p(a)/[p(a)+ p(b)] or p(b) = p(b)/[p(a)+p(b)] Where p(a) is number of favorable possibilities which can be true or false and p(b) is number of failures. And p(a)+p(b) is total probability of occurrence of event a. Now let us talk about probability of consecutive events. Consecutive events are those events which occur one after another, we can find the probability of these types of events by multiplying the probability of one consecutive event with other. Now we will take an example which can aid in understanding probability of consecutive events. Example: A die is rolled into the surface and a coin is tossed up in the air and a card is drawn from a pack of 52 cards consecutively. So find consecutive probability of getting 5 on die, head on coin and ace on card. Solution: firstly we will find the probabilities separately then we will combine them, Probability of getting 5 = 5/6, Probability of getting a head = 1/2 Probability of getting a ace = 4/52=1/13 Now for consecutive probability we have to multiply all these probabilities so our required result will be. Let us consider any event E, which is associated to some of the random experiment and is occur if the occurrence of any one of the elementary event is its outcome. If S is a sample space and a random experiment is performed. Then if E is any event, it means E is the subset of S. Then the probability of an occurrence of event E is defined as:

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P (E) = number of distinct elements of Event E / Number of distinct elements of sample S. We also know that S includes all possible outcomes of the event. Or we can write P (E) = n (E) / n (S) Let us take some example to understand the concept more clearly. Let’s take a pot with 10 blue balls and 90 red balls, which are of similar shape and size. Let us first mix the balls thoroughly and then one ball is drawn from the pot randomly. We come to the conclusion that the ball taken out from the pot will be either of blue color or of red color. As the number of red balls is much more than the number of blue balls, so this is more likely to get a Red Ball in compare to the Blue Ball. So we can say that the probability of getting a red ball is more likely than the probability of getting a blue color ball. This means event which is more likely to occur has higher probability as compared to the event which has less possibility of occurrence. Here we first count the total number of events = 90 + 10 = 100. We say that the probability of an occurrence of an event of getting a red ball = P( Red Ball ) = 90 / 100. And the probability of an occurrence of an event of getting a blue ball = P ( Blue Ball) = 10 /100.

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Consecutive Events