On a true-false quiz of six questions, Karen answers all the questions. What is the probability that she answers the first three
2 answers:
Answer: The probability of three correct answers and three incorrect answers is
Step-by-step explanation:
Since we have given that
There is a true - false quiz of six questions.
Probability of getting a true =
Probability of getting a false =
Probability that she answers the first three questions correctly and the last three questions incorrectly is given by
P(Three correct) × P(Three incorrect)
Hence, the probability of three correct answers and three incorrect answers is
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Using the hypergeometric distribution, it is found that there is a 0.4286 = 42.86% probability of getting 2 of the same colour.
The marbles are chosen without replacement, hence the <em>hypergeometric </em>distribution is used to solve this question.
<h3>What is the hypergeometric distribution formula?</h3>The formula is:
The parameters are:
- x is the number of successes.
- N is the size of the population.
- n is the size of the sample.
- k is the total number of desired outcomes.
In this problem:
- There is a total of 3 + 4 = 7 marbles, hence N = 7.
- Of those, 3 are blue, hence k = 3.
- 2 marbles will be taken, hence n = 2.
The probability of getting 2 of the same colour is the sum of P(X = 0), which is both red, with P(X = 2), which is both blue, then:
Hence:
0.4286 = 42.86% probability of getting 2 of the same colour.
You can learn more about the hypergeometric distribution at brainly.com/question/4818951