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In a carnival game, there are six identical boxes, one of which contains a prize. A contestant wins the prize by selecting the box containing it. Before each game, the old prize is removed and another prize is placed at random in one of the six boxes. Is it appropriate to use the binomial probability distribution to find the probability that a contestant who plays the game five times wins exactly twice? Check each of the requirements of a binomial experiment and give the values of n, r,and p.

Respuesta :

Answer:

Total probability is 0.1608

Explanation:

The Binomial Probability expression is:

∑(r=0 to n) [tex]C_{n,r} (P)^r ((-P)^{n-r})[/tex]

where

n = number of attempts

r = successes

P = Probability of each success and

-P = Probability of each Failure

We will sum all the the attempts to achieve the sum of 1 but

For this problem, we are looking for only one condition  which is  - playing the game five time and winning twice so P = [tex]\frac{1}{6}[/tex]  and -P = [tex]\frac{5}{6}[/tex]

So, our final solution is

[tex]C_{5,2} (\frac{1}{6})^2 ((\frac{5}{6})^{5-2})[/tex] = 0.1608 = 16.08%