Question

Series 4 Exercice 1 A farmer hybridizes flowers and gets the following results: 150 red flowers 200 green flowers 70 purple flowers 35 red and green flowers 20 red and purple flowers 12 green and purple flowers 6 red, green and purple flowers 30 without distinct colors 1- Construct a Venn diagram representing this situation 2. Determine the number of flowers who underwent the hybridization process 3- We choose a flower randomly. Using the Venn diagram, calculate the following probabilities: 2-) Probability to have flowers red and green but not purple b-) The probability that the flower has, at least, one of these three colors. - If we choose a flower who has a red color. How much is the probability that the flower has a purple color:

Answer 1

Given that there are

150 red, 200 green, 70 purple, 35 red and green flowers, 20 red and purple flowers, 12 green and purple flowers, 6 red, green and purple flowers 30 without distinct colors.

1- Construct a Venn diagram representing this situation?

For the given data the venn diagram can be constructed by as follows :

Total coloured flowers = R+G+P = 420

And total flowers = R+G+P+No distinct coloured= 450

2- Determine the number of flowers who underwent the hybridization process?

The number of flowers who underwent the hybridization process are multiple colours and with no distinct colours

i.e.20+6+12+35+30= 103

3- We choose a flower randomly. Using the venn diagram, calculate the following probabilities:

a-) Probability to have flowers red and green but not purple?

P(Red, Green Not Purple)= (Red flowers+Green flowers- (redgreen-redpurple-purplegreen)/Total flowers

= 277/450

b-) The probability that the flower has , at least one of these three colors?

P(atleast one of 3 colours)= (Total coloured flowers)/Total flowers

= 42/45