Question

A cooler contains nine bottles of sports drink: 4 lemon-lime flavored, 3 orange flavored, and 2

Answer 1

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 $0.08 \overline 3$

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, $P_F$ = F/n = 2/9

The probability of selecting a drink flavored orange given that a drink flavored fruit punch has already been selected is $P_{O(n_1)}$ = O/(n₁)

Where;

n₁ = n - 1 = 9 - 1 = 8

∴ $P_{O(n_1)}$ = 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 = $P_F$ × $P_{O(n_1)}$

∴ P = 2/9

$P = \dfrac{2}{9} \times \dfrac{3}{8} = \dfrac{6}{72} = \dfrac{1}{12}$

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$\overline 3$.