Determine the probability of event $$ E $$ if the odds against $$ E $$ are 7 to 12 . 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

Let the odds against $$ E $$ be given as 7 to 12. This means that the ratio of the probability that $$ E $$ does not occur to the probability that $$ E $$ occurs is

$$
\frac{P(\text{not }E)}{P(E)} = \frac{7}{12}.
$$

Since the sum of the probabilities is 1, we have

$$
P(E) + P(\text{not }E) = 1.
$$

Express $$ P(\text{not }E) $$ in terms of $$ P(E) $$:

$$
P(\text{not }E) = \frac{7}{12} P(E).
$$

Substitute into the total probability equation:

$$
P(E) + \frac{7}{12}P(E) = 1.
$$

Factor out $$ P(E) $$:

$$
\left(1 + \frac{7}{12}\right)P(E) = 1.
$$

Combine the terms:

$$
\frac{12}{12} + \frac{7}{12} = \frac{19}{12}.
$$

Then,

$$
\frac{19}{12} P(E) = 1.
$$

Solve for $$ P(E) $$:

$$
P(E) = \frac{12}{19}.
$$

To express this as a decimal, perform the division:

$$
\frac{12}{19} \approx 0.6316.
$$

Thus, the probability of event $$ E $$ is

$$
P(E) = \frac{12}{19} \approx 0.6316.
$$
The probability of event $$ E $$ is $$ \frac{12}{19} $$ or approximately 0.6316.

Determine the probability of event if the odds against are 7 to 12 .
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 against are 7 to 12 . 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.