I'm dumb I know, I need Probability help

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In summary, the conversation discusses two binomial distribution problems. The first one involves calculating the variance of the number of households that use coupons weekly among 10 randomly selected households making less than $25,000 annually. The second one involves finding the probability of selecting at most 1 brown M&M among 7 randomly selected M&Ms, given that 30% of all M&Ms are brown.
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r1terrell23
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I did this problem but am not too sure it's right, have a look

Of all households making less than $25,000 annually, 45% of them use coupons weekly when shopping for groceries. Suppose 10 households making less than $25,000 annually are selected at random. What is the variance of the number of households that use coupons weekly?

I got 4.5

But I have no clue how to do this one, the book doesn't explain anything

Suppose 30% of all M&Ms are brown. If 7 M&Ms are randomly selected, what is the probability that at most 1 is brown?
 
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These are both binomial distribution problems. The probability that a selected house hold uses coupons weekly is 0.45 and the probability that is does not is 0.55. You should have a formula for the variance of a sample from a binomial distribution.

If 30% of all M&Ms are brown, then 70% are not- the chance that any randomly selected M&M is not brown is 0.7. What is the probability that all 10 are not brown? What is the probability that exactly one is brown?
Again, this is a binomial distribution.
 

What is probability?

Probability is a mathematical concept that measures the likelihood of an event occurring. It is typically expressed as a number between 0 and 1, where 0 represents impossibility and 1 represents certainty.

Why is probability important?

Probability is important because it allows us to make predictions and decisions based on the likelihood of an event occurring. It is used in various fields such as science, economics, and statistics to analyze data and make informed decisions.

How do you calculate probability?

To calculate probability, you divide the number of favorable outcomes by the total number of possible outcomes. This can be represented as a fraction, decimal, or percentage.

What is the difference between theoretical and experimental probability?

Theoretical probability is based on mathematical calculations and assumes that all outcomes are equally likely. Experimental probability, on the other hand, is based on actual data collected from experiments or observations and may vary from theoretical probability.

How can probability be applied in real life?

Probability can be applied in various real-life situations, such as predicting weather patterns, analyzing stock market trends, or determining the likelihood of winning a game. It can also be used to make informed decisions in fields like healthcare, insurance, and sports.

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