PROBABILITY

[Audio] Presentation on probability Presented by K.N.Jeya.

[Audio] Definition Probability is a measure of how likely something will occur. It is ratio of desired outcomes to total outcomes. (#desired / # total) Probabilities of all outcomes sums to 1..

[Audio] Example If I roll number cube, there are six total possibilities.( 1,2, 3, 4, 5, 6) Each possibility has only one outcome, so each has a PROBABILITY of 1/6. For instance, the probability I roll a 2 is 1/6, since there is only a single 2 on the number cube..

[Audio] Practice If I flip a coin, what is the probability I get heads? What is the probability I get tails? Remember, to think of how many possibilities are there!.

[Audio] Answers P( heads) = ½ P( tails) = ½ If you add these two up, you will get 1, which means the answers are probably right..

TWO OR MORE EVENTS. If there are two or more events, you need to consider if it is happening at the same time or one after the other..

“ AND”. If the two events are happening at the same time, you need to multiply the two probabilities together. Usually, the questions use the word “AND” when describing the outcomes ..

“OR”. If the two events are happening one after the other, you need to add the two probabilities. Usually, the questions use the word “OR” when describing the outcomes..

PRACTICE. If I roll a number cube and flip a coin: What is the probability I will get a heads and a 6? What is the probability I will get a tails or a 3?.

ANSWERS. p(heads and 6) = 1/2 x 1/6 =1/12 P(tails or a 5) = 1/2 + 1/6 = 8/12 =2/3.

EXPERIMENTAL PROBABILITY. An experimental probability is one that happens as the result of an experiment. (# of outcomes) / (# of trials) The probabilities we have done so far are “theoretical probabilities”, because there was no experiments..

SURE OR CERTAIN EVENT. A sure event is an event, which always happens. An event which is sure to occur at every performance of an experiment is called a certain event connected with the experiment. Certain Events also known as Sure Event..

EXAMPLE. For example ,it's a sure event to obtain a number between 1 and 6 when rolling an ordinary die. The probability of a sure event has the value of 1. The probability of an impossible event has the value of 0..

EXAMPLE PROBLEM. The probability of a sure event is Answer: The value of the probability of an impossible event = 0 The value of the probability of a sure event = 1 An event is a sure event that always happens. Example: it’s a sure event to obtain a number between 1 n 6 when rolling an ordinary die..

IMPOSSIBLE EVENT. An event which cannot occur at any performance of the experiment is called an possible event. In other words, An event E is called an impossible event if P(E) = 0. This happens when no outcome of the experiment is a favourable outcome..

EXAMPLE. I n throwing a die, the event of getting a natural number greater than 6 is an impossible event ..

MUTUALLY EXCLUSIVE EVENTS. If there be no element common between two or more events, i.e., between two or more subsets of the sample space, then these events are called mutually exclusive events. If E 1 and E 2 are two mutually exclusive events, then E 1 ∩ E 2 = ∅.