Fiona has to choose a bouquet for her wedding. the probability that she uses red roses is 98%, the probability that she uses orchids is 87%, and the probability that she uses gerber daisies is 94%. given the probability that she has both roses and orchids is 0.87 and the probability that she has both gerber daisies and roses is 0.97 what is the probability that her bouquet contains roses or gerber daisies?

The events where you choose a bouquet containing roses is not mutually exclusive with the event where you choose a bouquet containing Gerber daises. The event that both flowers are present in the bouquet must subtracted from the sum of the probabilities that either roses or Gerber daisies are in the bouquet so,
P (roses or Gerber) = P (roses) + P (Gerber) - P(roses and Gerber)
P (roses or Gerber) = 0.98 + 0.94 - 0.97 = 0.95 or 95%