Kept getting the wrong answer? binomial conditional probability

In summary, the supposed coffee connoisseur claims to have a 75% chance of correctly distinguishing between instant and drip coffee. However, in a test with 5 cups, she must correctly identify at least 4 to have her claim granted. If she is only guessing, her chances of success would be 63.28%, calculated by multiplying the probability of exactly 4 correct guesses (0.75^4 * 0.25) by the probability of exactly 5 correct guesses (0.75^5). This calculation does not take into account the possibility of guessing correctly on more than 4 or 5 cups.
  • #1
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Product Testing A supposed coffee connoisseur claims she can distinguish between a cup of instant coffee and a cup of drip coffee 75% of the time. You give her 5 cups of coffee and tell her that you will grant her claim if she correctly identifies at least 4 of the 5 cups.

(a) What are her chances of having her claim granted if she is in fact only guessing?

i did
C(5,4)* .75^4 *.25 get the exactly 4 add .75^5 to get exactly 5.
i got 0.6328 but my online homework kept saying that it 's wrong.
 
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  • #2
Hint: consider what would be the probability of success if she was testing a single cup and only guessing.

Edit: this thread belongs in the homework forums
 

What is "Kept getting the wrong answer? binomial conditional probability"?

"Kept getting the wrong answer? binomial conditional probability" refers to a statistical calculation that measures the likelihood of a specific event occurring, given a certain set of conditions and a certain number of trials. It is often used to predict the outcome of binary events, such as heads or tails in a coin toss.

What is the formula for calculating binomial conditional probability?

The formula for calculating binomial conditional probability is P(x) = nCx * p^x * (1-p)^(n-x), where n is the number of trials, x is the number of successful outcomes, and p is the probability of success.

When is binomial conditional probability used?

Binomial conditional probability is used in various fields, such as biology, genetics, finance, and engineering, to predict the likelihood of an event occurring based on a set of conditions and a certain number of trials. It is often used in decision making and risk assessment.

What are some common mistakes when calculating binomial conditional probability?

Some common mistakes when calculating binomial conditional probability include using the wrong formula, using incorrect values for n and p, and not properly accounting for all possible outcomes. It is important to carefully define the conditions and trials in order to accurately calculate the probability.

How can I improve my understanding of binomial conditional probability?

To improve your understanding of binomial conditional probability, it is recommended to practice solving problems and working with different scenarios. You can also consult textbooks, online resources, and seek help from a tutor or mentor. Additionally, understanding the underlying concepts of probability theory can also enhance your understanding of binomial conditional probability.

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