Probability:
Probability is defined as the possibility of occurring the events in random. Probability is given by the ratio favorable outcome to the possible outcome.
Probability = `n/N`
Where
n = Number Of favorable outcome
N = Number of possible outcome
Odds
Odds is a part of probability, which is defined as the ratio of probability of events favorable outcome to the probability of unfavorable outcome.
Odds = `P/(1-P)`
Where
P= Probability
Odds is also given by
Number Of favorable outcome
Odds = --------------------------------------
Number of unfavorable outcome
Let us see the problems for probability and odds calculate in detailed clear explanation.
Example Problems for Probability Vs Odds
Problem for probability vs odds:
When dice are thrown random calculate the probability and odds value if the event occurred is 1, 4.
Solution:
Total number of events in a dice, N = 6
Number of events occurring 1, 4 in a dice, n = 2
Therefore number of favorable outcome = 2
Number of unfavorable outcome = 6-2 = 4
Probability = `n/N`
= `2/6`
Probability = `1/3`
Number Of favorable outcome
Odds= ----------------------------------------
Number of unfavorable outcome
=` 2/4`
Odds=`1/2`
Problem for probability vs odds:
When dice are thrown random, calculate the probability and odds value if the event occurred is not prime number.
Solution:
Total number of events in a dice, N = 6
Number of events occurring even numbers in a dice is not prime number = 2
Therefore number of favorable outcome = 2
Number of unfavorable outcome = 6-2 = 4
Probability = `n/N`
=`2/6`
Probability = `1/3`
Number Of favorable outcome
Odds= ----------------------------------------
Number of unfavorable outcome
= `2/4`
Odds = `1/2`
Problem for probability vs odds:
Calculate the odds if the probability of event occurring is 1/15
Solution:
Given, probability, P = `1/15`
The relation between even and odds is given in the formula,
Odds = `P/(1-P)`
= `(1/15)/(1-(1/15))`
= `( 1/15)/(14/15)`
= `(1/5)*(15/14)`
Odds = `1/14`
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