If the odds for pulling a prize out of the box are $3:4$, what is the probability of not pulling the prize out of the box? Express your answer as a common fraction.
If the odds for pulling a prize out of the box are $3:4$, that means that 3 out of 7 times will result in a prize, while 4 out of 7 times will not. So the probability of not pulling the prize out of the box is $\boxed{\frac{4}{7}}$.
\frac{4}{7}
Level 3
Counting & Probability
Problem: If the odds for pulling a prize out of the box are $3:4$, what is the probability of not pulling the prize out of the box? Express your answer as a common fraction.
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To find the probability of not pulling a prize, we first need to understand the given odds of pulling a prize, which are $3:4$. This means that for every 3 successful outcomes (pulling a prize), there are 4 unsuccessful outcomes (not pulling a prize). 

We can express the total number of outcomes as the sum of successful and unsuccessful outcomes. Therefore, the total outcomes are $3 + 4 = 7$.

Next, we calculate the probability of pulling a prize. The probability of pulling a prize is the ratio of successful outcomes to total outcomes, which is $\frac{3}{7}$.

To find the probability of not pulling a prize, we subtract the probability of pulling a prize from 1. This gives us:

Probability of not pulling a prize = 1 - Probability of pulling a prize
= 1 - $\frac{3}{7}$

To perform the subtraction, we convert 1 into a fraction with a denominator of 7:

1 = $\frac{7}{7}$

Now we can subtract:

Probability of not pulling a prize = $\frac{7}{7} - \frac{3}{7} = \frac{4}{7}$.

Thus, the final answer is $\frac{4}{7}$.<|END_OF_LATENT|> The final answer is $\frac{4}{7}$.