Question

a cooler contains 50 bottles; 30 bottles of water, which 8 are lemon flavored and 20 bottles of tea, of which 5 are lemon flavored. if you randomly select two beverages. what is the probability that both beverages are lemon flavored and 1 beverage is water and other is tea

Answer 1

The required probability is
`(13)/(50)`

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
`*` Probability of selecting a lemon bottle out of water bottles.

Probability of selecting a lemon flavored tea bottle = Probability of selecting a tea bottle
`*` Probability of selecting a lemon bottle out of tea bottles.

Formula for probability of an event E can be observed as:

`P(E) = \frac{\text{Number of favorable cases}}{\text {Total number of cases}}`

Probability of selecting a water bottle:

`(30)/(50) = (3)/(5)`

Probability of selecting a lemon flavored bottle from water bottle:

`(8)/(30)`

Probability of selecting a lemon flavored water bottle = P(A)

`(3)/(5) * (8)/(30) = (4)/(25)`

Probability of selecting a tea bottle:

`(20)/(50) = (2)/(5)`

Probability of selecting a lemon flavored bottle from tea bottle:

`(5)/(20) = (1)/(4)`

Probability of selecting a lemon flavored tea bottle = P(B)

`(2)/(5) * (1)/(4) = (1)/(10)`

The required probability is:

P(A) + P(B):

`(4)/(25) + (1)/(10)\\\Rightarrow (8+5)/(50)\\\Rightarrow (13)/(50)`