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09 Jan 2020, 19:42
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45% (02:37) correct
55%
(02:29)
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based on 78
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A test has 5 multiple-choice questions. Each question has 4 answer options (A,B,C,D). What is the probability that a student will choose “B” for at least four questions if no questions are left blank?
A) 1/256
B) 5/1024
C) 1/64
D) 21/1024
E) 1/16
A) 1/256
B) 5/1024
C) 1/64
D) 21/1024
E) 1/16
10 Jan 2020, 02:31
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In this question on probability, we need to understand two things:
#1 – Any of the four/five questions can have the answer as B, so we need to select those four/five questions.
#2 – The probability of getting B as the right answer is ¼ and that of not getting B as the right answer is ¾.
The number of ways of selecting any 4 questions of 5 = \(5_C_4\) = 5. In each of these 5 cases, the probability that the student will choose B as an answer is ¼ and the probability that he will not choose B is ¾.
Therefore, probability that the student will choose B for 4 questions = 5 * \((\frac{1}{4})^4\) * (\(\frac{3}{4}\)) = \(\frac{15 }{ 1024}\).
The number of ways of selecting all 5 questions of 5 = \(5_C_5\) = 1.
Therefore, probability that the student will choose B for all 5 questions = 1 * \((\frac{1}{4})^5\) * \((\frac{3}{4})^0\) = \(\frac{1 }{ 1024}\).
The total probability =\( \frac{15 }{ 1024}\) + \(\frac{1 }{ 1024}\) = \(\frac{16 }{ 1024}\) = \(\frac{1 }{ 64}\).
The correct answer option is C.
Hope that helps!
#1 – Any of the four/five questions can have the answer as B, so we need to select those four/five questions.
#2 – The probability of getting B as the right answer is ¼ and that of not getting B as the right answer is ¾.
The number of ways of selecting any 4 questions of 5 = \(5_C_4\) = 5. In each of these 5 cases, the probability that the student will choose B as an answer is ¼ and the probability that he will not choose B is ¾.
Therefore, probability that the student will choose B for 4 questions = 5 * \((\frac{1}{4})^4\) * (\(\frac{3}{4}\)) = \(\frac{15 }{ 1024}\).
The number of ways of selecting all 5 questions of 5 = \(5_C_5\) = 1.
Therefore, probability that the student will choose B for all 5 questions = 1 * \((\frac{1}{4})^5\) * \((\frac{3}{4})^0\) = \(\frac{1 }{ 1024}\).
The total probability =\( \frac{15 }{ 1024}\) + \(\frac{1 }{ 1024}\) = \(\frac{16 }{ 1024}\) = \(\frac{1 }{ 64}\).
The correct answer option is C.
Hope that helps!
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