Stats Binomial Dist to solve

In summary, The problem given involves finding the probability of at most one brown M&M out of a selection of seven. The conversation discusses using Binomial Distribution to solve it, with initial attempts using probabilities of 0 and 1, but realizing the need to switch the probabilities. The final solution involves using the formula for Binomial Distribution with n=7, p=0.3, and q=0.7.
  • #1
r1terrell23
2
0
Okay so I did this problem and got it wrong but I get one more chance to get it right. I tried using Binomial Dist to solve it but I failed.

30% of all M&Ms are brown. If 7 M&Ms are randomly selected, what is the probability that at most 1 is brown?

I thought I would use 0 and 1 but I guess not. Can someone help me?
 
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  • #2
p0=.37
p1=7*.36*.7

Add them up.
 
  • #3
Sorry, got the probs reversed. switch .3 and .7.

p0=.77
p1=7*.76*.3

Add them up.
 
  • #4
For Binomial Distribution,
take n=7, p=0.3, q=1-p=0.7.

P(X<=1)=P(X=0)+P(X=1)=q^7+n*p*q^6

thts it gys...
enjy
 

1. What is the binomial distribution used for in statistics?

The binomial distribution is used to model the probability of a certain number of successes in a fixed number of independent trials, where each trial has only two possible outcomes (success or failure) and the probability of success remains constant. It is commonly used in surveys, experiments, and other statistical analyses.

2. How do you calculate the probability of a specific number of successes in a binomial distribution?

To calculate the probability of a specific number of successes in a binomial distribution, you can use the binomial probability formula: P(X = k) = nCk * p^k * (1-p)^(n-k), where n is the number of trials, p is the probability of success, and k is the number of successes. You can also use a statistical software or calculator to find this probability.

3. What is the difference between a binomial distribution and a normal distribution?

A binomial distribution is used for discrete data with two possible outcomes, while a normal distribution is used for continuous data with a bell-shaped curve. In a binomial distribution, the probability of success remains constant for each trial, while in a normal distribution, the probability can vary. Additionally, a binomial distribution is bounded by a fixed number of trials, while a normal distribution is unbounded.

4. How can you use the binomial distribution to solve real-world problems?

The binomial distribution can be used to solve a variety of real-world problems, such as predicting the success rate of a new product launch, estimating the number of defective items in a production batch, or determining the likelihood of a medical treatment being effective. By understanding the probability of success and the number of trials, you can use the binomial distribution to make informed decisions and predictions.

5. Are there any assumptions or limitations when using the binomial distribution?

Yes, there are a few assumptions and limitations when using the binomial distribution. These include: the trials must be independent, the probability of success must remain constant for each trial, and the number of trials must be fixed. It is also important to note that the binomial distribution is not appropriate for data that is continuous or has more than two possible outcomes.

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