In a lottery game, a single ball is drawn at random from a container that contains 25 identical balls numbered from 1 through 25 . Use the equation $P(A \cup B)=P(A)+P(B)-P(A \cap B)$, where $A$ and $B$ are any events, to compute the probability that the number drawn is prime or greater than 6 . The probability that the number drawn is prime or greater than 6 is (Type an integer or a decimal.)

Step 1 ：Identify the prime numbers between 1 and 25. The prime numbers are \(2, 3, 5, 7, 11, 13, 17, 19, 23\).

Step 2 ：Identify the numbers greater than 6. The numbers are \(7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25\).

Step 3 ：Calculate the probability of each event separately. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of outcomes. In this case, the total number of outcomes is 25 because there are 25 balls.

Step 4 ：The probability of drawing a prime number, denoted as \(P(A)\), is \(\frac{9}{25} = 0.36\).

Step 5 ：The probability of drawing a number greater than 6, denoted as \(P(B)\), is \(\frac{19}{25} = 0.76\).

Step 6 ：Identify the intersection of the two events, which is the set of numbers that are both prime and greater than 6. The intersection is \(7, 11, 13, 17, 19, 23\).

Step 7 ：The probability of drawing a number that is both prime and greater than 6, denoted as \(P(A \cap B)\), is \(\frac{6}{25} = 0.24\).

Step 8 ：Use the formula \(P(A \cup B)=P(A)+P(B)-P(A \cap B)\) to calculate the probability of the union of the two events.

Step 9 ：Subtract the probability of the intersection from the sum of the probabilities of each event to avoid double counting. The probability of drawing a number that is either prime or greater than 6, denoted as \(P(A \cup B)\), is \(0.36 + 0.76 - 0.24 = 0.88\).

Step 10 ：Final Answer: The probability that the number drawn is prime or greater than 6 is \(\boxed{0.88}\).