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

Answer:

The probability of choosing 3 sodas and 4 water is;

$0.385$

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;

$P=\frac{^{ns}C_{rs}\times^{nw}C_{rw}}{^{nt}C_{rt}}$

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;

$\begin{gathered} P=\frac{^{ns}C_{rs}\times^{nw}C_{rw}}{^{nt}P_{rt}} \\ P=\frac{^7C_3\times^9C_4}{^{16}C_7} \end{gathered}$

solving for P;

$\begin{gathered} P=\frac{(\frac{7!}{4!3!})\times(\frac{9!}{5!4!})}{(\frac{16!}{9!7!})}=\frac{4410}{11440} \\ P=\frac{441}{1144} \\ P=0.385 \end{gathered}$

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

$0.385$