In a large vase, there are 8 roses,

Question

5 daisies, 12 lilies, and 9 orchids. If 4 flowers are selected
at random, and not replaced, find the probability that at
least 1 of the flowers is a rose. Would you consider this
event likely to occur? Explain your answer.

Answer 1

consider the case where you pick only roses

Prob( all roses) = C(8,4)/C(34,4)
= 70/46376
= 35/23188
So the prob of selecting at least 1 rose = 1 - 35/23188
= 23153/23188 or appr .9985

Highly likely to happen.

Answer 2

seems to me you want 1 - prob(no roses)
rather than 1 - prob(all roses)