Respuesta :
Answer:
The probability that out of the nine drinks in the cooler, one of the two friends selects a drink flavored fruit punch after which the next of the two friends selects a drink flavored orange is [tex]0.08 \overline 3[/tex]
Step-by-step explanation:
The given parameters for the content of the cooler are;
The total number of bottles of sports drink in the cooler, n = 9 bottles
The number of lemon-lime flavored bottles of sports drink in the cooler, L = 4 bottles
The number of orange flavored bottles of sports drink in the cooler in the cooler, O = 3 bottles
The number of fruit punch flavored bottles of sports drink in the cooler, F = 2 bottles
The probability of selecting a drink flavored fruit punch, [tex]P_F[/tex] = F/n = 2/9
The probability of selecting a drink flavored orange given that a drink flavored fruit punch has already been selected is [tex]P_{O(n_1)}[/tex] = O/(n₁)
Where;
n₁ = n - 1 = 9 - 1 = 8
∴ [tex]P_{O(n_1)}[/tex] = O/(n₁) = O/(n - 1) = 3/(9 - 1) = 3/8
Therefore, the probability that the first of two friends to select a drink got a drink flavored fruit punch and the second of the two friends got a drink flavored orange is, P = [tex]P_F[/tex] × [tex]P_{O(n_1)}[/tex]
∴ P = 2/9
[tex]P = \dfrac{2}{9} \times \dfrac{3}{8} = \dfrac{6}{72} = \dfrac{1}{12}[/tex]
The probability that one of two friends selects a drink flavored fruit punch and the next of the two friends selected a drink flavored orange is P = 1/12 = 0.08[tex]\overline 3[/tex].
