Question

The probability of Rory randomly picking a specific flower out of a bouquet

is shown in the table below.
What is the probability that he doesn't pick a rose or a lily?
Give your answer as a fraction in its simplest form.
Probability of choosing flowers:

P (Rose) - 1/4
P (Lily) - 5/9
P (Neither) - ?

Answer 1

Picking neither is the opposite of picking a rose or a lily.

We know that
`P(A)=1-P(A')`.

Therefore:

`P(\text{Neither})=1-(P(\text{Rose})+P(\text{Lily}))\\P(\text{Neither})=1-\left((1)/(4)+(5)/(9)\right)\\P(\text{Neither})=1-\left((9)/(36)+(20)/(36)\right)\\P(\text{Neither})=1-(29)/(36)\\P(\text{Neither})=(7)/(36)`