Simple Probability problem

Question

A box contains papers numbered 1 to 8. Two slips are drawn, one after the other without replacement.

a) What is the probability that both numbers are even? (and for my sake why)

b) The first number drawn is a five and the second is composite? (a small explanation)

Answer 1

Assuming that the 'slips' are those papers numbered 1 through 8, then, w/o replacement, P(even,even)= (4/8)(3/7) because, initially, there are four even numbered slips of paper, after which three of the remaining seven are even.  This computation gives answer + reasons.

 

P(5, then composite #) = (1/8)(3/7) because, after selecting the one & only 'five' there remain only numbers 1,2,3,4,6,7,8 and of these, only three [4,6,8] are composites.