Suppose the P(A) = 1/6 . Find the odds in favor of A .
Would you explain the step by step process?
thanks!
P(A) = 1/6
P(not A) = 5/6
odds if favour of A = 1/6 : 5/6 = 1 : 5
Oh, odds in favor of A, huh? Well, let's dive into it step by step, shall we?
Step 1: Determine the probability of A occurring. In this case, P(A) is given as 1/6.
Step 2: Calculate the probability of not A (denoted as P(not A)). Since there are only two outcomes - A or not A - the probability of not A can be found using the complement rule: P(not A) = 1 - P(A). In this case, P(not A) = 1 - 1/6 = 5/6.
Step 3: Divide the probability of A by the probability of not A to find the odds in favor of A. In other words, odds in favor of A = P(A) / P(not A) = (1/6) / (5/6) = 1/5.
So, the odds in favor of event A happening would be 1 to 5.
Certainly! To find the odds in favor of event A, we need to calculate the probability of A occurring divided by the probability of A not occurring.
Given that P(A) = 1/6, we can determine the probability of A not occurring by subtracting P(A) from 1:
P(A') = 1 - P(A) = 1 - 1/6 = 5/6
Now, to calculate the odds in favor of A, we divide the probability of A by the probability of A not occurring:
Odds in favor of A = P(A) / P(A') = (1/6) / (5/6)
To simplify the calculation, we can multiply the numerator and denominator by the reciprocal of the denominator:
Odds in favor of A = (1/6) * (6/5) = 1/5
Therefore, the odds in favor of A are 1 to 5 or 1:5.
Certainly! To find the odds in favor of an event A, we need to compare the probability of A occurring to the probability of A not occurring. In this case, we are given that P(A) = 1/6, which represents the probability of event A occurring.
Step 1: Find the probability of A not occurring.
Since there are only two outcomes - event A occurring or not occurring - we know that the total probability is equal to 1. Therefore, to find the probability of A not occurring, we subtract the probability of A from 1.
P(A') = 1 - P(A)
= 1 - 1/6
= 5/6
Step 2: Calculate the odds in favor of A.
The odds in favor of A are given by the ratio of the probability of A occurring to the probability of A not occurring.
Odds in favor of A = P(A) / P(A')
= (1/6) / (5/6)
= (1/6) * (6/5)
= 1/5
Therefore, the odds in favor of A are 1/5.
In summary, to find the odds in favor of an event A:
1. Calculate the probability of A not occurring by subtracting P(A) from 1.
2. Divide the probability of A by the probability of A not occurring to obtain the odds in favor of A.