In a survey of exotic plants in a botanical garden, the events S S\,S and F F\,F are defined as follows: S S\,S is the event that a plant is a succulent and F F\,F is the event that a plant is a flowering species. The probabilities are given by
P(S)=310P(S∪F)=2950 P(S) = \frac{3}{10} \quad P(S \cup F) = \frac{29}{50} P(S)=103P(S∪F)=5029Given that S S\,S and F F\,F are independent,
show that P(F)=25\displaystyle P(F) = \frac{2}{5}P(F)=52
The event X X\,X represents the plant belonging to a rare genus such that
P(X)=0.06P(S∩X)=P(X) P(X) = 0.06 \quad P(S \cap X) = P(X) P(X)=0.06P(S∩X)=P(X)Find P(X′∣S)P(X' | S)P(X′∣S)
Given that F F\,F and X X\,X are mutually exclusive,
draw a Venn diagram to represent the events SSS, FFF, and XXX, giving the exact probabilities of each of the five regions within the circles and the region outside the circles.
