SOLUTION: A garden has 8 white roses and 11 red roses. One rose is plucked from the garden and then one more rose is plucked, without replacement. Let the event W = plucking a white r

Question 893857: A garden has 8 white roses and 11 red roses. One rose is plucked from the garden and then one more rose is plucked, without replacement.
Let the event W = plucking a white rose.
and event R = plucking a red rose.
In two or more complete sentences, explain the meaning of probabilities P(R/W) and P(W/R). Do they have same value?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
garden has 8 white roses and 11 red roses.
one rose is plucked form the garden and then one more rose is plucked with replacement.

W = event of plucking a white rose.
R = event of plucking a red rose.

Explain the meaning of the probabilities of p(W/R) and P(R/W).
Do they have the same value?

P(W/R) means find the probability of W given R.
P(R/W) means find the probability of R given W.

since the two events are done without replacement, the probabilities for each will be different on the second draw than the first draw.

For the first draw, the probabilities are:

p(R) = 11/19
p(W) = 8/19

For the second draw, the probabilities are:

p(R) given that white was plucked on the first draw = 11/18
p(W) given that red was plucked on the first draw = 8/18

the numerator is the same as on the first draw because neither of the flowers being picked on the second draw were also picked on the first draw.

the denominator is different because there is one less flower to pluck.

the probabilities are clearly not the same.

p(R/W) = 11/18
p(W/R) = 8/18

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