Question

A box contains 8 cards numbered 2, 3, 4, 5, 6* 7, 8, 9. One card is selected at random and replaced. What is the probability that you can select a 2 and then a prime number?

Answer 1

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:

`P(2\text{and prime)=P(2)xP(prime)}`

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:

`P(2)=(1)/(8)`

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:

`P(\text{prime)}=(4)/(8)=(1)/(2)`

Therefore, the probability of getting a 2 and a prime number is:

`P(2andprime)=(1)/(8)*(1)/(2)=(1)/(16)`