Study Calculate Probability

Study calculates probability assumption has its origin in games of opportunity pertaining to gamble. Jerome Cardon an Italian mathematician wrote book on ‘Games of chance’ published in 1663. Study calculates probability is given by ratio of number of favorable outcomes, n to the number of possible outcomes. Power of statistical test is probability that test reject a false null hypothesis.

Frequently used terms in probability

Frequently used terms in probability

Experiment:      
Experiment is defined as a process for which its result is clear.

Sample space:      
Possible outcomes in experiment are called sample space.

Event:          
Each non-empty subset of sample space is an event.

Mutually exclusive events (or disjoint events):        

If two or more events have no simple events is known as mutually exclusive.

Exhaustive events:        

If no event occurs outside set of events it is recognized as exhaustive event of set. And one of events in that set must occur as answer of an experiment.

Equally likely events:        

Equally expected events is the one in which a set of events will not occur in preference to other.

Examples for study calculate probability

Ex 1:   Study calculate probability that a girl get access in Engineering college is 0.80, study calculate probability that she obtain admittance in Medical College is 0.88, and the probability that she will get both is 0.72. Calculate study probability that (i) She will get at-least one of the two seats (ii) She will get only one of two seats

Sol :  Let I be event of receiving admission in Engineering college and M be event of getting

admission in Medical College.

P(I) = 0.80, P(M) = 0.88 and P(I ∩ M) = 0.72

(i) P (at-least one of the two seats)

= P(I or M) = P(I ∪ M)

= P(I) + P(M) − P(I ∩ M)

= 0.80 + 0.88 − 0.72

= 0.96

(ii) P(only one of two seats) = P[only I or only M].

= P[(I ∩ ) ∪ (  ∩ M)]

= P(I ∩ ) + P( ∩ M)

= {P(I)−P(I∩M)}+{P(M)−P(I∩M)}

= {0.80 − 0.72} + {0.88 − 0.72}

= 0.08 + 0.16

= 0.24

Probability is 0.24.

Ex 2:  P(A)=12,P(B)=18 and P(A ∪ B)=10 calculate P(A ∩ B)

Sol :   P(A ∩ B)=  P(A)+P(B) - P(A ∪ B)

=12+18-10

P(A ∩ B)=20