Answer:
The required probability is ![\dfrac{13}{50}](https://tex.z-dn.net/?f=%5Cdfrac%7B13%7D%7B50%7D)
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
<em>Probability of selecting a lemon flavored water bottle = Probability of selecting a water bottle </em>
<em> Probability of selecting a lemon bottle out of water bottles.</em>
<em></em>
<em>Probability of selecting a lemon flavored tea bottle = Probability of selecting a tea bottle </em>
<em> Probability of selecting a lemon bottle out of tea bottles.</em>
Formula for probability of an event E can be observed as:
![P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}](https://tex.z-dn.net/?f=P%28E%29%20%3D%20%5Cdfrac%7B%5Ctext%7BNumber%20of%20favorable%20cases%7D%7D%7B%5Ctext%20%7BTotal%20number%20of%20cases%7D%7D)
Probability of selecting a water bottle:
![\dfrac{30}{50} = \dfrac{3}{5}](https://tex.z-dn.net/?f=%5Cdfrac%7B30%7D%7B50%7D%20%3D%20%5Cdfrac%7B3%7D%7B5%7D)
Probability of selecting a lemon flavored bottle from water bottle:
![\dfrac{8}{30}](https://tex.z-dn.net/?f=%5Cdfrac%7B8%7D%7B30%7D)
<em>Probability of selecting a lemon flavored water bottle = P(A)</em>
<em></em>
<em></em>
<em></em>
Probability of selecting a tea bottle:
![\dfrac{20}{50} = \dfrac{2}{5}](https://tex.z-dn.net/?f=%5Cdfrac%7B20%7D%7B50%7D%20%3D%20%5Cdfrac%7B2%7D%7B5%7D)
Probability of selecting a lemon flavored bottle from tea bottle:
![\dfrac{5}{20} = \dfrac{1}{4}](https://tex.z-dn.net/?f=%5Cdfrac%7B5%7D%7B20%7D%20%3D%20%5Cdfrac%7B1%7D%7B4%7D)
<em>Probability of selecting a lemon flavored tea bottle = P(B)</em>
<em></em>
<em></em>
<em></em>
<em>The required probability is:</em>
<em>P(A) + P(B):</em>
<em></em>
<em></em>