Question

isaac's favorite cereal is running a promotion that says 111-in-444 boxes of the cereal contains a prize. suppose that isaac is going to buy 666 boxes of this cereal, and let xxx represent the number of prizes he wins in these boxes. assume that these boxes represent a random sample, and assume that prizes are independent between boxes. what is the probability that he wins exactly 222 prizes in the 666 boxes? you may round your answer to the nearest hundredth.

Answer 1

Using the binomial distribution, there is a 0.6328 = 63.28% probability that she wins at most 1 prize.

For each box, there are only two possible outcomes, either it has a prize, or it does not. The probability of a box having a prize is independent of any other box, hence, the binomial distribution is used to solve this question.

Binomial probability distribution

The parameters are:

x is the number of successes.

n is the number of trials.

p is the probability of a success on a single trial.

In this problem:

She buys 5 boxes, hence

1 in 4 boxes has a prize, hence

The probability is:

P ( X ≤ 1 ) =P ( X = 0 ) + P ( X = 1 )

Then ,

P ( X ≤ 1 ) = P ( X = 0 ) + P ( X = 1 )

= 0.2373 + 0.3955

= 0.6328

Thus 0.6328 = 63.28% probability that she wins at most 1 prize

To know more about binomial distribution you may go through the link which is mentioned below:

https://brainly.com/question/14565246

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