Answer :
We are given that a box contains cards numbered 2, 3, 4, 5, 6, 7, 8, 9. To determine the probability of getting a 2 and a prime number is equal to the product of getting a 2 and the probability of getting a prime number, that is:
[tex]P(2\text{and prime)=P(2)xP(prime)}[/tex]The probability of getting a2 is equal to the quotient of the number of cards numbered 2 and the total number of cards, that is:
[tex]P(2)=\frac{1}{8}[/tex]The probability of getting a prime number is equal to the number of cards with a prime number and the total number of cards. The cards with a prime number are: 2, 3, 5, 7,. therefore, the probability of getting a prime number is:
[tex]P(\text{prime)}=\frac{4}{8}=\frac{1}{2}[/tex]Therefore, the probability of getting a 2 and a prime number is:
[tex]P(2andprime)=\frac{1}{8}\times\frac{1}{2}=\frac{1}{16}[/tex]