Question

Based on the data in this two-way table, which statement is true? Type of Flower/Color Red Pink Yellow Total Rose 40 20 45 105 Hibiscus 80 40 90 210 Total 120 60 135 315 A flower being pink and a flower being a rose are independent of each other. A flower being pink is dependent on a flower being a rose. A flower being a rose is dependent on a flower being pink. A flower being pink and a flower being a rose are the same. NextReset

Answer 1

A. a flower being pink and a flower being a rose are independent of each other.

Explanation:

Type of Flower/Color Red Pink Yellow Total

Rose 40 20 45 105

Hibiscus 80 40 90 210

Total 120 60 135 315

Now the probability, if the flower is pink =
`(60)/(315)=(4)/(21)`

The probability that the flower is rose =
`(105)/(315)=(1)/(3)`

Te probability that flower is pink and rose =
`(20)/(315)`=
`(4)/(63)`

Also we can see,
`(4)/(21) * (1)/(3) =(4)/(63)`

Therefore, we can state that events are independent.

Hence, option A is correct.