You are given the probability of event E. Find the odds in favor of event E and the odds against event E.
a. 1/8
b. 2/5
Prob(E) = 1/8
prob(notE) = 7/8
odds against the event = (7/8) : (1/8) = 7 : 8
do the other one the same way.
To find the odds in favor of event E, you need to calculate the probability of event E occurring divided by the probability of event E not occurring.
Let's calculate the odds in favor of event E for each given probability:
a. Probability of event E = 1/8
Probability of event E not occurring = 1 - 1/8 = 7/8
The odds in favor of event E = (Probability of event E) / (Probability of event E not occurring) = (1/8) / (7/8) = 1/7
Therefore, the odds in favor of event E are 1/7.
b. Probability of event E = 2/5
Probability of event E not occurring = 1 - 2/5 = 3/5
The odds in favor of event E = (Probability of event E) / (Probability of event E not occurring) = (2/5) / (3/5) = 2/3
Therefore, the odds in favor of event E are 2/3.
To find the odds against event E, you need to calculate the probability of event E not occurring divided by the probability of event E occurring.
Using the same probabilities as above:
a. The odds against event E = (Probability of event E not occurring) / (Probability of event E) = (7/8) / (1/8) = 7/1 = 7
Therefore, the odds against event E are 7.
b. The odds against event E = (Probability of event E not occurring) / (Probability of event E) = (3/5) / (2/5) = 3/2
Therefore, the odds against event E are 3/2.
To find the odds in favor of event E, you can use the formula:
Odds in favor of E = P(E) / (1 - P(E))
For option a, the probability is given as 1/8. Plugging this value into the formula:
Odds in favor of E = (1/8) / (1 - (1/8))
= (1/8) / (7/8)
= 1/7
Therefore, the odds in favor of event E for option a are 1/7.
To find the odds against event E, you can use the formula:
Odds against E = (1 - P(E)) / P(E)
For option a:
Odds against E = (1 - (1/8)) / (1/8)
= (7/8) / (1/8)
= 7/1
= 7
Therefore, the odds against event E for option a are 7.
Now let's move on to option b.
For option b, the probability is given as 2/5.
Odds in favor of E = (2/5) / (1 - (2/5))
= (2/5) / (3/5)
= 2/3
Therefore, the odds in favor of event E for option b are 2/3.
Odds against E = (1 - P(E)) / P(E)
= (1 - (2/5)) / (2/5)
= (3/5) / (2/5)
= 3/2
Therefore, the odds against event E for option b are 3/2.