Subjects probability

Coffee Probability 75Acc2

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1. **Stating the problem:** We are given that the probability a randomly selected U.S. adult drinks coffee on a given day is $0.56$. 2. **Explain what this probability means:** The probability $0.56$ means that if you randomly pick one U.S. adult, there is a 56% chance that this person drinks coffee on that day. It is a measure of likelihood, not a guarantee. 3. **If a researcher surveys 100 U.S. adults, will exactly 56 have consumed coffee?** No, not necessarily. The number 56 is the expected value (mean) of coffee drinkers in a sample of 100 adults, calculated as: $$\text{Expected number} = 100 \times 0.56 = 56$$ 4. **Why not exactly 56?** Because the actual number of coffee drinkers in the sample follows a binomial distribution with parameters $n=100$ and $p=0.56$. The number can vary around 56 due to randomness. 5. **Summary:** - Probability $0.56$ means 56% chance for any one adult. - In 100 adults, the average number drinking coffee is 56. - The exact number can be more or less than 56 in any particular survey.