Answer:
To determine the probability that a randomly picked card from the set \(\{2, 3, 4, 5, 6, 7, 8, 9\}\) is a prime number, we first identify which numbers in the set are prime. Prime numbers are defined as numbers greater than 1 that have no positive divisors other than 1 and themselves.
We check each number in the set:
- \(2\) is prime (divisors: 1, 2)
- \(3\) is prime (divisors: 1, 3)
- \(4\) is not prime (divisors: 1, 2, 4)
- \(5\) is prime (divisors: 1, 5)
- \(6\) is not prime (divisors: 1, 2, 3, 6)
- \(7\) is prime (divisors: 1, 7)
- \(8\) is not prime (divisors: 1, 2, 4, 8)
- \(9\) is not prime (divisors: 1, 3, 9)
The prime numbers in the set are \(\{2, 3, 5, 7\}\). Thus, there are 4 prime numbers out of a total of 8 numbers in the set.
The probability \(P\) that a randomly picked card is prime is calculated as follows:
\[
P(\text{prime}) = \frac{\text{Number of prime numbers}}{\text{Total number of cards}} = \frac{4}{8} = \frac{1}{2}
\]
To convert this probability to a percentage, we multiply by 100:
\[
P(\text{prime}) \times 100 = \frac{1}{2} \times 100 = 50\%
\]
Thus, the probability that a randomly picked card is prime is \(50\%\).
