To be hired by a company, an applicant should pass two tests The first test contains 10 questions, and for each question, the probability of giving a correct answer is p 1 The second test contains 20 questions, and for each question of this test, the probability of a correct answer is p 2 Whether a...

To be hired by a company, an applicant should pass two tests. The first test contains 10

Question:

To be hired by a company, an applicant should pass two tests. The first test contains 10 questions, and for each question, the probability of giving a correct answer is p₁. The second test contains 20 questions, and for each question of this test, the probability of a correct answer is p₂. Whether an answer is correct does not depend on the answers to other questions. To pass each test one should answer correctly at least a half of questions.

(a) Find the probability that the applicant will pass both tests. (The formula you should get may contain the symbol Σ.)

(b) Arrange a file in Excel for computing the answer for given p₁ and p₂.

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