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If the odds against an event are 7 : 3, what is the probability that the event will occur?
0.3
0.7
0.4
0.6
0.3
If odds against are a:b, then probability is simply the second number divided by the sum of both numbers: b/(a+b).
The odds against an event are given as 7:3.
P(E)=total┬аoutcomesfavorable┬аoutcomesтАЛ=a+bbтАЛ
If odds against are a:b, then probability is simply the second number divided by the sum of both numbers: b/(a+b).
Students frequently mistake the given ratio 7:3 for probability itself and incorrectly choose 0.7 or 0.3 without summing the parts.
Define given variables
Given the odds against an event are a:b=7:3, where a=7 represents the number of unfavorable outcomes and b=3 represents the number of favorable outcomes.
a=7,b=3
Apply probability formula
The probability of an event occurring is given by the ratio of favorable outcomes to the total outcomes (a+b).
P(E)=a+bbтАЛ
Perform calculation
Substitute the values into the formula: P(E)=3/(7+3)=3/10=0.3.
P(E)=103тАЛ=0.3
A is correct because the probability is the ratio of favorable outcomes to the total, which is 3/(7+3)=0.3.
This concept is fundamental to Bayesian statistics and risk assessment in quantitative finance, where odds ratios are frequently converted to probabilities.