Question

from a bag of 50 cards, whose faces are numbered 1 to 50, one card is drawn at random. what is the probability of getting a 1, 7 or 29 or an even number?

Explanation:

Step1: Identify favorable outcomes

First, find the number of even numbers from 1 to 50. The formula for the number of even numbers between 1 and \(n\) is \(\frac{n}{2}\) (when \(n\) is even). So for \(n = 50\), the number of even numbers is \(\frac{50}{2}=25\). Then we also have the numbers 1, 7, 29. So total favorable outcomes \(= 25 + 3=28\) (since 1, 7, 29 are odd and not included in the even numbers).

Step2: Calculate probability

The probability \(P\) is given by the formula \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). The total number of cards is 50. So \(P = \frac{28}{50}\). Simplify this fraction by dividing numerator and denominator by 2: \(\frac{28\div2}{50\div2}=\frac{14}{25}\).

Answer:

\(\frac{14}{25}\)