Question

A cooler contains four colas, seven root beers, and four ginger ales. Three people grab a drink at random, one at a time.a) What is the probability that the first person grabs a cola, the second person grabs a ginger ale, and the third person grabs a cola? b) What is the probability that the third person grabs a root beer given that the first two grabbed colas?

Answer 1

Given:

• Number of colas = 4

,

• Number of robot beers = 7

,

• Number of ginger ales = 4

Where:

Total number if drinks = 4 + 7 + 4 = 15

Given that 3 people grab a drink at random, one at a time.

Let's solve for the following:

• (a). What is the probability that the first person grabs a cola, the second person grabs a ginger ale, and the third person grabs a cola?

• Probability the first person grabs a cola is:

$P(first\text{ cola\rparen=}\frac{number\text{ of colas}}{total\text{ number of drinks}}=\frac{4}{15}$

• Probability second person grabs a ginger is:

$P(second\text{ ginger\rparen=}\frac{number\text{ of ginger ales}}{total\text{ number -1}}=\frac{4}{15-1}=\frac{4}{14}=\frac{2}{7}$

The probability the third prson grabs a cola is:

$P(third\text{ cola\rparen=}\frac{4-1}{15-2}=\frac{3}{13}$

Therefore, the total probability will be:

$\begin{gathered} P=\frac{4}{15}*\frac{2}{7}*\frac{3}{13} \\ \\ P=\frac{4*2*3}{15*7*13} \\ \\ P=\frac{24}{1365} \\ \\ P=\frac{8}{455} \end{gathered}$

Therefore, the probability that the first person grabs a cola, the second person grabs a ginger ale, and the third person grabs a cola is 8/455.

• (b). What is the probability that the third person grabs a root beer given that the first two grabbed colas?

The probability will be:

$\begin{gathered} P=\frac{4}{15}*\frac{3}{14}*\frac{7}{13} \\ \\ P=\frac{4*3*7}{15*14*13} \\ \\ P=\frac{84}{2730} \\ \\ P=\frac{2}{65} \end{gathered}$

Therefore, the probability that the third person grabs a root beer given that the first two grabbed colas is 2/65.

ANSWER:

• (a). 8/455

• (b). 2/65