Question

a box contains ten cards labeled q, r, s, t, u, v, w, x, y, and z. one card will be randomly chosen. what is the probability of choosing a letter from q to t? write your answer as a fraction in simplest form.

Explanation:

Step1: Determine the number of favorable outcomes

The letters from Q to T are Q, R, S, T. So there are 4 favorable outcomes.

Step2: Determine the total number of outcomes

There are 10 cards in total (labeled Q, R, S, T, U, V, W, X, Y, Z).

Step3: Calculate the probability

The probability formula is \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). Substituting the values, we get \(P = \frac{4}{10}\).

Step4: Simplify the fraction

Divide both the numerator and denominator by their greatest common divisor, which is 2. So \(\frac{4\div2}{10\div2}=\frac{2}{5}\).

Answer:

\(\frac{2}{5}\)