Question

there are cards in a jar numbered 54 to 73. what is the probability of a random draw of an even number greater than 60?

Explanation:

Step1: Calculate total number of cards

The formula for the number of integers from \(a\) to \(b\) (inclusive) is \(b - a+1\). Here \(a = 54\) and \(b = 73\), so the total number of cards \(n_{total}=73 - 54 + 1=20\).

Step2: Find number of even - numbered cards greater than 60

The even numbers greater than 60 and between 54 and 73 are 62, 64, 66, 68, 70, 72. So \(n_{favorable}=6\).

Step3: Calculate probability

The probability formula is \(P=\frac{n_{favorable}}{n_{total}}\). Substituting the values, \(P=\frac{6}{20}=0.3 = 30\%\).

Answer:

30%