Any Time Padhai Academy Probability Important terminology (part-1)

(i)Random experiment: It is a process which results in an outcome which is one of the various possible outcomes that are known to us before hand e.g. throwing of a die is a random experiment as it leads to fall of one of the outcome from (1, 2, 3, 4, 5, 6). Similarly taking a card from a pack of 52 cards is also a random experiment. (ii)Sample space: It is the set of all possible outcomes of a random experiment e.g. (H, T is the sample space associated with tossing of a coin. In set notation it can be interpreted as the universal set.

Example # : Write the sample space of the experiment 'A coin is tossed and a die is thrown, Solution : The sample space S = {H 1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6). Example # : Write the sample space of the experiment 'A coin is tossed, if it shows head a coin tossed again else a die is thrown Solution The sample space S (HH, HT, T1, T2, T3, T4, T5, T6)

Find the sample space associated with the experiment of rolling a pair of dice (plural of die) once. Also find the number of elements of the sample space. Example # : 2 4 6 2 (2,1) 2, 2) 2, 3) 2,4) (2, 5) (2, 6) 3 (3, 1) (3, 2) (3, 3) 3,4) (3, 5) (3, 6) 4 6 6,1) (6, 2) 6, 3) 6,4) 6,5 6, 6) Figure Number of elements (outcomes) of the above sample space is 6 x 6 i.e., 36

(ii) Event It is subset of sample space. e.g. getting a head in tossing a coin or getting a prime number in throwing a die. In general if a sample space consists 'n' elements, then a maximum of 2 events can be associated with it (iv) Complement of event The complement of an event 'A' with respect to a sample space S is the set of all elements of 'S which are not in A. It is usually denoted by A', A or AC

(v) Simple event If an event covers only one point of sample space, then it is called a simple event e.g. getting a head followed by a tail in throwing of a coin 2 times is a simple event. (vi) Compound event When two or more than two events occur simultaneously, the event is said to be a compound event. Symbolically A B or AB represent the occurrence of both A & B simultaneously. Note "Au B" or A + B represent the occurrence of either A or B.

Example # : Write down all the events of the experiment tossing of a coin. Solution : S-{H, T} the events are , {H), (T), {H, T} Example # : A die is thrown. Let A be the event' an odd number turns up, and B be the event'a number divisible by 3 turns up'. Write the events (a) A or B (b) A and B A Solution : [1, 3, 5), B 3(3, 6} A or B AuB (1, 3, 5, 6) A and B An B(3)

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Anurag Singh Katheria

3 years ago

Sir,thank you for this commendable job. But, Sir plz give the examples also.
It will be very helpful.

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Goldberg 12

8 months ago

thank u so much sir and sir pls vector and 3d next

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Tirtha Sarathi

8 months ago

sir iit jee ja question k upor video banaya

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Shashank Sati

8 months ago

sir more questions please.......

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