Question

1. If ​P(E)=0.17​, find the odds in favor of E. What are the odds in favor of​ E? Select the correct choice below and fill in the answer​ box(es) to complete your answer.

2. If​ P(E)=0.29​, find the odds against E
3. Compute the probability of event E if the odds in favor of E are 10 to 27
4. If the odds against event E are 13 to 7​, what is the probability of​ E?

Answer 1

The odds in favor of an event E with P(E)=0.17 are approximately 1 to 5, whereas for P(E)=0.29, the odds against E are about 7 to 2. The probability of event E when odds in favor are 10 to 27 is approximately 0.27, and with odds against of 13 to 7, the probability is 0.35.

Step-by-step explanation:

1. If P(E)=0.17, the odds in favor of E are calculated by taking the probability of E occurring and dividing it by the probability of E not occurring. Since the probability of E not occurring is 1 - P(E) = 1 - 0.17 = 0.83, the odds in favor of E are 0.17 / 0.83, which simplifies to approximately 1 to 5.

2. If P(E)=0.29, the odds against E are found by dividing the probability of E not occurring by the probability of E occurring. Thus, the odds against E are (1 - 0.29) / 0.29 = 0.71 / 0.29, which simplifies to approximately 7 to 2.

3. Given the odds in favor of E are 10 to 27, to compute the probability of event E, we use the total number of outcomes, which is the sum of the odds (10 + 27 = 37). Thus, P(E) = number in favor / total number = 10 / 37 ≈ 0.27.

4. If the odds against event E are 13 to 7, the probability of E is found by using the numbers that represent the odds. The total outcomes are 13 (against) + 7 (in favor) = 20. Therefore, the probability of E is the number in favor divided by the total, or 7 / 20, which is 0.35.

Answer 2

To find the odds in favor of event E, use P(E) / (1 - P(E)). The odds against E can be found by subtracting the probability of E from 1. To compute the probability of E given the odds in favor, use odds in favor E / (odds in favor E + 1). If the odds against E are given, subtract the probability of not E from 1 to find the probability of E.

Step-by-step explanation:

To find the odds in favor of event E, we use the formula:

Odds in favor of E = P(E) / (1 - P(E))

Substituting P(E) = 0.17 into the formula, we get:

Odds in favor of E = 0.17 / (1 - 0.17) = 0.17 / 0.83 = 17/83

Therefore, the odds in favor of event E are 17 to 83.

To find the odds against event E, we subtract the probability of E from 1:

Odds against E = 1 - P(E)

Substituting P(E) = 0.29 into the formula, we get:

Odds against E = 1 - 0.29 = 0.71

Therefore, the odds against event E are 71 to 29.

To compute the probability of event E if the odds in favor of E are 10 to 27, we use the formula:

Probability of E = odds in favor of E / (odds in favor of E + 1)

Substituting the given odds in favor of E = 10 to 27, we get:

Probability of E = 10 / (10 + 27) = 10/37

Therefore, the probability of event E is 10/37.

If the odds against event E are 13 to 7, we subtract the probability of E from 1 to find the probability of not E. Then, we subtract the probability of not E from 1 to get the probability of E:

Probability of not E = 13 / (13 + 7) = 13/20

Probability of E = 1 - 13/20 = 7/20

Therefore, the probability of event E is 7/20.