Question

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 for the first time and event r=plucking a red rose for the second time in two or more complete sentences explain the meaning of probabilities p(r/w) and p(w/r) do they have the same value

Answer 1

P(r/w) is the probability of picking a red rose at first picking and a white rose at second picking.
P(w/r) is the probability of picking a white rose at first picking and a red rose at second picking.

P(r/w) = $\frac{11}{19}$×$\frac{8}{18}$ = $\frac{88}{342}$
P(w/r) = $\frac{8}{19}$×$\frac{11}{18}$=$\frac{88}{342}$

Notice that the second fraction is out of 18 because the second picking of rose will be out of 18 since the first rose is not replaced.

P(r/w) equals to P(w/r)