Given 5 roses, 8 daisies, 7 lilies, and 5 orchids.
Total number of flowers = 5 + 8 + 7 + 5 = 25 flowers
Total number of flowers minus rose = 8 +7 + 5 =20 flowers
If 4 flowers are selected and not replaced, the probability that at least one of the flowers is a rose
The probability formula is:
[tex]P(E)=\frac{N\text{(Required outcome)}}{N(\text{possible outcome)}}[/tex][tex]\begin{gathered} P(at\text{ least one is rose)= 1 - }P(\text{no rose)} \\ P(no\text{ rose)=}\frac{20C_4}{25C_4} \\ =0.3830 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} P(at\text{ least one is rose) = 1 - 0.3830} \\ =\text{ 0.6170} \end{gathered}[/tex]The Probability that at least one of the flowers is a rose is 0.617
