Determine the probability of event $$ E $$ if the odds for (i.e., in favor of) $$ E $$ are 14 to 5. Note:For any final answer that has up to four decimal places, enter your answer without rounding the number. For any answers with more than four decimal values, round your final answer to four decimal places.

Question

UpStudy AI · Accepted Answer

To determine the probability of event $$ E $$ when the odds for $$ E $$ are 14 to 5, we can use the formula for odds to find the probability.

Given odds for $$ E $$ are 14 to 5, we can express this as a ratio of the number of favorable outcomes to the number of unfavorable outcomes. Let's denote the number of favorable outcomes as $$ F $$ and the number of unfavorable outcomes as $$ U $$.

The odds for $$ E $$ can be expressed as $$ \frac{F}{U} = \frac{14}{5} $$.

The probability of event $$ E $$ is given by the formula:
$$ P(E) = \frac{F}{F + U} $$

We can substitute the values of $$ F $$ and $$ U $$ from the odds ratio into the formula to find the probability of event $$ E $$.

Let's calculate the probability of event $$ E $$ using the given odds ratio.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{14}{5}$$
The odds for event $$ E $$ are 14 to 5, which can be simplified to 2.8.

Now, we can use this value to find the probability of event $$ E $$ using the formula:
$$ P(E) = \frac{F}{F + U} $$

Substitute the value of $$ \frac{F}{U} = 2.8 $$ into the formula to find the probability of event $$ E $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{2.8}{\left(2.8+1\right)}$$
- step1: Remove the parentheses:
  $$\frac{2.8}{2.8+1}$$
- step2: Add the numbers:
  $$\frac{2.8}{3.8}$$
- step3: Convert the expressions:
  $$\frac{\frac{14}{5}}{\frac{19}{5}}$$
- step4: Multiply by the reciprocal:
  $$\frac{14}{5}\times \frac{5}{19}$$
- step5: Reduce the numbers:
  $$14\times \frac{1}{19}$$
- step6: Multiply:
  $$\frac{14}{19}$$
The probability of event $$ E $$ is approximately 0.736842.
The probability of event $$ E $$ is approximately 0.7368.

Determine the probability of event if the odds for (i.e., in favor of) are 14 to
5.
Note:For any final answer that has up to four decimal places, enter your answer without rounding
the number. For any answers with more than four decimal values, round your final answer to four
decimal places.

Solución de inteligencia artificial de Upstudy

Responder

Solución

The Deep Dive

preguntas relacionadas

Latest Probability Questions

Determine the probability of event if the odds for (i.e., in favor of) are 14 to 5. Note:For any final answer that has up to four decimal places, enter your answer without rounding the number. For any answers with more than four decimal values, round your final answer to four decimal places.