Answer: 0.26
Step-by-step explanation:
Binomial probability formula :-
[tex]P(X=x)=^nC_x\ p^x\ (1-p)^{n-x}[/tex], where P(x) is the probability of getting success in x trials , n is total number of trials and p is the probability of getting success in each trial.
Given : The probability of winning = [tex]\dfrac{1}{6}[/tex]
Let X be the random variable that represents the number of sodas.
Since he is guaranteed that he will win one soda .
If Cody buys 6 sodas, then the probability that he will win at least one more soda will be :
[tex]P(x\geq2 )=1-(P(0)+P(1))\\\\=1-(^6C_0\ (\dfrac{1}{6})^0\ (1-\dfrac{1}{6})^{6-0}+^6C_1\ (\dfrac{1}{6})^1\ (1-\dfrac{1}{6})^{6-1})\\\\=1-((\dfrac{5}{6})^6+(\dfrac{5}{6})^5)\approx0.26[/tex]
Hence, the true probability he will win at least one more soda =0.26
