Answer:
The required probability is [tex]\dfrac{13}{50}[/tex]
Step-by-step explanation:
Total number of bottles = 50
Total number of water bottles = 30
Total number of lemon flavored water bottles = 8
Total number of tea bottles = 20
Total number of lemon flavored tea bottles = 5
Probability of selecting a lemon flavored water bottle = Probability of selecting a water bottle [tex]\times[/tex] Probability of selecting a lemon bottle out of water bottles.
Probability of selecting a lemon flavored tea bottle = Probability of selecting a tea bottle [tex]\times[/tex] Probability of selecting a lemon bottle out of tea bottles.
Formula for probability of an event E can be observed as:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
Probability of selecting a water bottle:
[tex]\dfrac{30}{50} = \dfrac{3}{5}[/tex]
Probability of selecting a lemon flavored bottle from water bottle:
[tex]\dfrac{8}{30}[/tex]
Probability of selecting a lemon flavored water bottle = P(A)
[tex]\dfrac{3}{5} \times \dfrac{8}{30} = \dfrac{4}{25}[/tex]
Probability of selecting a tea bottle:
[tex]\dfrac{20}{50} = \dfrac{2}{5}[/tex]
Probability of selecting a lemon flavored bottle from tea bottle:
[tex]\dfrac{5}{20} = \dfrac{1}{4}[/tex]
Probability of selecting a lemon flavored tea bottle = P(B)
[tex]\dfrac{2}{5} \times \dfrac{1}{4} = \dfrac{1}{10}[/tex]
The required probability is:
P(A) + P(B):
[tex]\dfrac{4}{25} + \dfrac{1}{10}\\\Rightarrow \dfrac{8+5}{50}\\\Rightarrow \dfrac{13}{50}[/tex]
