What is probability ?
Probability is the likelihood that an event will occur under a set of given conditions. The probability of an event occurring has a value between 0 and 1
If an event E is defined in a sample space S then its mathematical
form is:
𝑃 (𝐴) = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑎𝑚𝑝𝑙𝑒𝑠 𝑝𝑜𝑖𝑛𝑡𝑠 𝑖𝑛 𝐴 / 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑎𝑚𝑝𝑙𝑒𝑠 𝑝𝑜𝑖𝑛𝑡𝑠 𝑖𝑛 𝑆 = n(E) / n (S)
What is event ?
An event is an individual outcome or any number of outcomes (sample points) of a random experiment.
A set consisting of all possible outcomes that can result from a random experiment:
e.g. the experiment of tossing a coin results in either of two possible outcomes, a Heads (H) or a Tails (T).
So the sample space for this experiment may be expressed as S={H,T}
Question # 1 :
A die is rolled find the probability that an even number is obtained.
Answer # 1 :
The sample space S is
S={1,2,3,4,5,6}
Let E be event of even number
E={2,4,6}
The probability is
P(E)= 𝑛(𝐸) / n(S) = 3/6 = 1/2
Question # 2 :
A coin is tossed three times what is the probability that at least one Tails appears?
Answer # 2 :
S={HHH,HHT,HTH,THH,HTT,THT,TTH,TTT}
𝑛(𝑆 )= 8
Let E be an event that at least one Heads appears then
E ={HHT,HTH,THH,HTT,THT,TTH,TTT}
𝑛(E) = 7
P(E)= 𝑛(E) / n (S) = 7/8