Question

you have four cards, labeled 2-5. what is the probability of drawing a number less than 3, putting the card back, then drawing a prime number?

Answer 1

`(3)/(16)`

Explanation:

Cards which are available are numbered as: {2, 3, 4, 5}

Number of cards available = 4

Selecting a number less than 3:

There is only one number less than 3, so only 1 way of selecting a card numbered less than 3. Therefore, the probability of selecting a card less than 3 =
`(1)/(3)`

Since this card is placed back, the total number of cards in the sample remain the same.

Selecting a prime number:

There are 3 prime numbers in the sample: 2,3 and 5

Probability of selecting a prime numbers would be 3 out 4 i.e. =
`(3)/(4)`

The two above mentioned events are independent of each other, so the probability of occurrence of both will be the product of their individual probabilities i.e.

Probability of drawing a number less than 3, putting the card back, then drawing a prime number =
`(1)/(4) * (3)/(4) = (3)/(16)`