Answer to Question #129264 in Statistics and Probability for Alia Aziz

Question

A box contains 10 red and 12 white rose flowers. Flowers are picked up at random one by one without replacement. What is probability that
a) The first 3 flowers are red.
b) Flowers are in alternate order starting from 1st one is red.

Answer 1

a) Probability that the first 3 flowers are red:

P $=\frac{10}{22}*\frac{9}{21}*\frac{8}{20}=0.078$

b) Flowers are in alternate order starting from 1st one is red.

The question is not clear how many flowers are picked. However, it can be interpreted in one of two ways.

i) All flowers from the box are picked

ii) Three flowers are picked from the box(just like part a)

If all the flowers are picked, the probability that flowers are picked in alternate order is zero. After 20 flowers have been picked, there will be no red lowers left in the box, while there will be two white flowers. Since the probability of picking a red flower is zero, then the probability that the flower are picked in alternating order is zero.

P(Flowers are in alternate order starting from 1st one is red if three flowers are picked)

P =$\frac{10}{22}*\frac{12}{21}*\frac{9}{20}=0.1169$