Q:

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?

Accepted Solution

A:
Answer:[tex]\frac{3}{16}[/tex]Step-by-step explanation:Cards which are available are numbered as: {2, 3, 4, 5}Number of cards available = 4Selecting 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 = [tex]\frac{1}{3}[/tex]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 5Probability of selecting a prime numbers would be 3 out 4 i.e. = [tex]\frac{3}{4}[/tex]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 = [tex]\frac{1}{4} \times \frac{3}{4} = \frac{3}{16}[/tex]