Question

A florist running a special: pick the number of flowers you want, and they will arrange a random bouquet out of the roses in inventory. When you call, they have 4 white roses, 5 red roses, and 6 pink roses in inventory. In two or more sentences, with your answers in fraction form, find the value and explain the meaning for p( w | r) and p(r | r) do they have the same value? Why or why not?

Answer 1

The conditional probability p(w | r) and p(r | r) both have the same value of 2/7 because after picking a red rose, the chances of picking a white or another red rose out of the remaining flowers are equal.

Step-by-step explanation:

The question involves calculating conditional probabilities using the concepts of probability in mathematics.

The conditional probability p(w | r) represents the probability of picking a white rose given that a red rose has already been picked.

The probability p(r | r) refers to the probability of picking a red rose given that a red rose has already been picked.

To calculate these, we consider the total number of roses: 4 white + 5 red + 6 pink = 15 roses.

For p(w | r), if a red rose is picked, there are now 14 roses left, and still 4 white ones, so p(w | r) = 4/14. For p(r | r), if a red rose is picked first, there are now 4 red roses left out of the 14, so p(r | r) = 4/14.

We see that both p(w | r) and p(r | r) have the same value, which is 4/14 or 2/7 when simplified.

This is because the probability of picking a white rose or another red rose are equal after the first red rose is taken, since the same number of white roses and remaining red roses are available for the second pick.