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$A box contains ten cards labeled Q,R,S,T,U,V,W,X,Y, and Z. One card will be randomly chosen. What is the probability. of choosing a letter from U to Z ? Write your answer as a fraction in simplest form.$

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 $U$ to $Z$ ? $\newline$ Write your answer as a fraction in simplest form.

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Probability of simple events

Full solution

Q. 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

U

to

Z

?

\newline

Write your answer as a fraction in simplest form.

Total Possible Outcomes: Determine the total number of possible outcomes when choosing one card from the box. $\newline$ Since there are $10$ cards labeled from $Q$ to $Z$ , there are $10$ possible outcomes when choosing one card.
Favorable Outcomes: Identify the favorable outcomes for the event of choosing a card with a letter from $U$ to $Z$ . The cards labeled from $U$ to $Z$ are $U$ , $V$ , $W$ , $X$ , $Y$ , and $Z$ . That gives us $Z$ $0$ favorable outcomes.
Calculate Probability: Calculate the probability of choosing a card with a letter from U to Z. $\newline$ Probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. $\newline$ So, the probability $P$ is $P = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$ .
Perform Calculation: Perform the calculation using the numbers identified in the previous steps. $\newline$ $P = \frac{6 \text{ (favorable outcomes)}}{10 \text{ (total possible outcomes)}} = \frac{3}{5}$ after simplifying the fraction.

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