Question

In a large vase, there are 5 roses, 8 daisies, 7 lilies, and 5 orchids. If 4 flowers are selected at random, and not replaced, find the probability that at least one of the flowers is a rose.

Answer 1

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:

`P(E)=\frac{N\text{(Required outcome)}}{N(\text{possible outcome)}}`
`\begin{gathered} P(at\text{ least one is rose)= 1 - }P(\text{no rose)} \\ P(no\text{ rose)=}(20C_4)/(25C_4) \\ =0.3830 \end{gathered}`

Therefore,

`\begin{gathered} P(at\text{ least one is rose) = 1 - 0.3830} \\ =\text{ 0.6170} \end{gathered}`

The Probability that at least one of the flowers is a rose is 0.617