In a carnival game there are six identical boxes one of whic

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.

Solution

YES.

It is because the probability of winning everytime is constant, that is 1/6.

Also, the games are independent, as prizes are randomly placed and selected.

The number of trials is fixed as well.

Thus, here,

n = 5
p = 1/6 or 0.16666666667
r = 2 [ANSWERS]