if the probability that an identified hurricane will make a direct hit on a certain stretch of beach is 0.20, what are the odds against a direct hit?
1 : 0.20 I :19 i think its like this way?
1.0 - 0.2 = 0.8
The concept of odds is slightly different from probablity
the odds in favour of some event
= prob of the event happening : prob of the event NOT happening
so, prob of direct hit = .2
prob of no direct hit = .8
odds in favour of no direct hit = .8 : .2
= 8:2
= 4 : 1
To calculate the odds against a direct hit, you need to divide the probability of a direct hit not occurring by the probability of a direct hit occurring.
In this case, the probability of a direct hit is given as 0.20. To get the probability of a direct hit not occurring, which is the complement of the given probability, subtract the probability of a direct hit from 1.
1 - 0.20 = 0.80
So, the probability of a direct hit not occurring is 0.80.
To express this as odds against a direct hit, you can now write it as a ratio comparing the probability of a direct hit not occurring to the probability of a direct hit occurring:
0.80 : 0.20
This can also be simplified to:
4 : 1
So, the odds against a direct hit on the stretch of beach are 4 to 1.