FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 9.15Event Prior Probability Conditional Probability Joint Probability Posterior Probability
B 1 21 3/10 3/20 3/4B 2 21 1/10 1/20 1/4
1 4/10 19.6 ODDSWe must know the concept of odds. The word odd is frequently used in statistics. Odds relate the chances
in favour of an event to the chances against it. For instance, the odds are 2 : 1 that A will get a job, means
that there are 2 chances that he will get the job and 1 chance against his getting the job. This can also be
converted into probability as getting the job = 2/3. Therefore, if the odds are a : b in favour of an event then
P(A) = a/(a+b). Further, it may be noted that the odds are a : b in favour of an event is the same as to say
that the odds are b : a against the event.
If the probability of an event is p, then the odds in favour of its occurrence are P to (1-p) and the odds
against its occurrence are 1-p to p.
Example 19 :
Suppose it is 11 to 5 against a person who is now 38 years of age living till he is 73 and 5 to 3 against B who
is 43 Living till he is 78, find the chance that at least one of these persons will be alive 35 years hence.
Solution :
The probability that A will die within 35 years = 1611
The probability that B will die within 35 years = 85
The probability that both of them will die within 35 years
11 5 55
=16 8 128× =The probability that both of them will not die i.e.
atleast one of them will be alive
1 55 73
= −128 128=or^73 100 57%
128 × =Example 20 :
Two cards are drawn at random from a well-shuffled pack of 52 cards. What is the probability that :
(a) both are aces,
(b) both are red,
(c) at least one is an ace?