Let's solve the problem step by step.
1. Identify the total number of outcomes: The box contains ten cards labeled Q, R, S, T, U, V, W, X, Y, and Z. Therefore, there are 10 possible outcomes when choosing one card from the box.
2. Identify the favorable outcomes: We are interested in the probability of choosing a card labeled from U to Z. The cards that meet this criteria are U, V, W, X, Y, and Z. Count the number of these cards:
- U
- V
- W
- X
- Y
- Z
There are 6 favorable outcomes here.
3. Calculate the probability: The probability of an event is given by the ratio of the number of favorable outcomes to the total number of possible outcomes. Therefore,
[tex]\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}
\][/tex]
Substituting the numbers we identified:
[tex]\[
\text{Probability} = \frac{6}{10}
= \frac{3}{5}
\][/tex]
So, the probability of choosing a card with a letter from U to Z is [tex]\( \frac{3}{5} \)[/tex].
