Question

In Ali's cooler there are 7 bottles of soda and 9 bottles of water. Ali is going to choose 7 bottles at random from the cooler to give to his friends. What is the probability that he will choose 3 sodas and 4 waters? Round your answer to three decimal places.

Answer 1

The probability of choosing 3 sodas and 4 water is;

`0.385`

Step-by-step explanation:

Given that Ali's cooler there are 7 bottles of soda and 9 bottles of water.

And Ali needs to choose 7 bottles at random, the probability that he chooses 3 soda and 4 bottles of water is;

`P=(^(ns)C_(rs)*^(nw)C_(rw))/(^(nt)C_(rt))`

Note;

number of soda ns = 7

number of water nw = 9

The total number of options to select from is; 7 + 9 nt = 16

Number of soda selected rs= 3

number water selected rw= 4

Total number of bottles selected = 3+4 rt= 7

Substituting the given values;

`\begin{gathered} P=(^(ns)C_(rs)*^(nw)C_(rw))/(^(nt)P_(rt)) \\ P=(^7C_3*^9C_4)/(^(16)C_7) \end{gathered}`

solving for P;

`\begin{gathered} P=(((7!)/(4!3!))*((9!)/(5!4!)))/(((16!)/(9!7!)))=(4410)/(11440) \\ P=(441)/(1144) \\ P=0.385 \end{gathered}`

Therefore, the probability of choosing 3 sodas and 4 water is;

`0.385`