Answer :
a). P(contains Raspberry) + P(contains Kiwi) = 11/15
b). P(contains Raspberry or Kiwi) = 3/5
c). Choosing a smoothie containing Raspberry and choosing a smoothie containing Kiwi are not mutually exclusive events.
a). From the Venn diagram, Raspberry = 10, Kiwi = 12 and the total possible outcome = 30 so;
P(contains Raspberry) = 10/30
P(contains Kiwi) = 12/30
P(contains Raspberry) + P(contains Kiwi) = 10/30 + 12/30 = 11/15
b). We shall represent Raspberry and Kiwi with R and K respectively so that;
P(contains Raspberry or Kiwi) = P(R) + P(K) - P(R ∩ K)
P(R or K) = 11/15 - 4/30
P(R or K) = 18/30
P(R or K) = 3/5
c). Since P(contains Raspberry) + P(contains Kiwi) is not equal to P(contains Raspberry or Kiwi), that is 11/15 ≠ 3/5, Choosing a smoothie containing Raspberry and choosing a smoothie containing Kiwi are not mutually exclusive events.
Therefore, P(contains Raspberry) + P(contains Kiwi) is equal to 11/15, P(contains Raspberry or Kiwi) is equal to 3/5 and choosing a smoothie containing Raspberry and choosing a smoothie containing Kiwi are not mutually exclusive events.
