Question

A flower vase has 5 white lilies, 4 pink roses, and 6 yellow carnations. One flower is chosen at random and given to a woman for her to keep. Another flower is then chosen at random and given to a different woman for her to keep. Both women received a pink rose. Are these events independent or dependent?

A) Dependent because the women both received a pink rose.
B) Independent because the women both received a pink rose.
C) Dependent because when the first flower is taken, it affects the ratio of the types of flowers in the vase.
D) Independent because when the first flower is taken, it does not change the ratio of the types of flowers in the vase.

Answer 1

It C because when u take away 2 it affects how many flowers are left

Answer 2

Option C - Dependent because when the first flower is taken, it affects the ratio of the types of flowers in the vase.

Explanation:

Given : A flower vase has 5 white lilies, 4 pink roses, and 6 yellow carnations.

One flower is chosen at random and given to a woman for her to keep.

Another flower is then chosen at random and given to a different woman for her to keep. Both women received a pink rose.

To find : Are these events independent or dependent?

Solution :

According to the statements,

The probability that the second woman receives a pink rose is dependent upon what the first woman receives.

Total flowers = 5+4+6=15

If the first woman does not receive a pink rose,

Then, the probability of the second woman receiving one is
`(4)/(15)`

If the first woman does receive a pink rose

Then, the probability of the second woman receiving one is
`(3)/(15)=(1)/(5)`

Therefore, Option C is correct.

Dependent because when the first flower is taken, it affects the ratio of the types of flowers in the vase.