A test consists of 10 true/false questions

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A test consists of 10 true/false questions

First problem: A test consists of 10 true/false questions. To pass the test a student must answer at least 6 questions correctly. If a student guesses on each question, what is the probability that the student will pass the test?

A test consists of 10 true/false questions

Second problem:
In a certain college, 33% of the physics majors belong to ethnic minorities. If 10 students are selected at random from the physics majors, what is the probability that no more than 6 belong to an ethnic minority?
I know the answer is .982 but don’t know how to explain how to do it and how to punch it in calculator

Third problem
Find the probability of at least 2 girls in 7 births. Assume that male and female births are equally likely and that the births are independent events.

Fourth problem:
The brand name of a certain chain of coffee shops has a 54% recognition rate in the town of Coffleton. An executive from the company wants to verify the recognition rate as the company is interested in opening a coffee shop in the town. He selects a random sample of 10 Coffleton residents. Find the probability that exactly 4 of the 10 Coffleton residents recognize the brand name.

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