Question

Cody buys a soda that offers another soda free if he is lucky. The cap reads '1 in 6 wins!', meaning that each soda has a 1/6 probability of winning. Cody sees this and buys six of these sodas, thinking he is guaranteed a seventh. What is the true probability he will win at least one more soda? Express your answer as decimal to the nearest hundredth.

Answer 1

stop cheating

Explanation:

Answer 2

Answer: 0.26

Explanation:

Binomial probability formula :-

`P(X=x)=^nC_x\ p^x\ (1-p)^(n-x)`, 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 =
`(1)/(6)`

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 :

`P(x\geq2 )=1-(P(0)+P(1))\\\\=1-(^6C_0\ ((1)/(6))^0\ (1-(1)/(6))^(6-0)+^6C_1\ ((1)/(6))^1\ (1-(1)/(6))^(6-1))\\\\=1-(((5)/(6))^6+((5)/(6))^5)\approx0.26`

Hence, the true probability he will win at least one more soda =0.26