Constructing sample spaces:
Sample space is generally denoted by S, Ω or U. Fundamentally it’s the set of all random trials; like in tossing a coin the sample space is (head, tail). If we toss two coins then sample space for this random trial is (head, head), (head, tail), (tail, head), (tail, tail). In the trial of tossing a single sided die sample space s is (1, 2, 3, 4, 5, and 6). It’s not necessary that one trial should have only one sample space; like in a trial of drawing a card from a standard deck of 52 playing cards one probability of outcome is could be the rank (ace through king) and the another sample space could be suits i.e. (club, diamond, hearts or spades). The subsets of sample space are called event. Problems would be critical after increasing the number of sample spaces. So it would be problematic when there are infinite sample spaces means there are infinite events.
Sample space construction:
Sample space is the set of all possible outcomes and it’s necessary to consider all possibilities. It may be a difficult task and for this purpose counting principle can be used. If there is more than one event it’s important to determine all possibilities that exist. It can be stated that:
“If there are A ways of an event to occur and B ways for occurrence of second event then there are A.B ways for both to occur”. This is the concept of the counting principle.
An example is given below which can help to understand sample space better. (know more about cbse sample papers, here)
Example: one jar contains 1 red, 3 green, 2 blue or 4 yellow balls. Then what would be the probability of each outcome if a single ball is chosen from the jar.
Solution: Sample space for this random trial is
S = (red, green, blue, yellow)
Probability can be calculated as:
Probability: P (red ball) = 1/10
P (green ball) = 3/10
P (blue ball) = 2/10 = 1/5
P (yellow ball) = 4/10 = 2/5
In the next session we will discuss about Sampling errors.
Sample space is generally denoted by S, Ω or U. Fundamentally it’s the set of all random trials; like in tossing a coin the sample space is (head, tail). If we toss two coins then sample space for this random trial is (head, head), (head, tail), (tail, head), (tail, tail). In the trial of tossing a single sided die sample space s is (1, 2, 3, 4, 5, and 6). It’s not necessary that one trial should have only one sample space; like in a trial of drawing a card from a standard deck of 52 playing cards one probability of outcome is could be the rank (ace through king) and the another sample space could be suits i.e. (club, diamond, hearts or spades). The subsets of sample space are called event. Problems would be critical after increasing the number of sample spaces. So it would be problematic when there are infinite sample spaces means there are infinite events.
Sample space construction:
Sample space is the set of all possible outcomes and it’s necessary to consider all possibilities. It may be a difficult task and for this purpose counting principle can be used. If there is more than one event it’s important to determine all possibilities that exist. It can be stated that:
“If there are A ways of an event to occur and B ways for occurrence of second event then there are A.B ways for both to occur”. This is the concept of the counting principle.
An example is given below which can help to understand sample space better. (know more about cbse sample papers, here)
Example: one jar contains 1 red, 3 green, 2 blue or 4 yellow balls. Then what would be the probability of each outcome if a single ball is chosen from the jar.
Solution: Sample space for this random trial is
S = (red, green, blue, yellow)
Probability can be calculated as:
Probability: P (red ball) = 1/10
P (green ball) = 3/10
P (blue ball) = 2/10 = 1/5
P (yellow ball) = 4/10 = 2/5
In the next session we will discuss about Sampling errors.
