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A Ph.D. student visits three research stations X, Y and Z in a random order to collect samples. The probability that the student visits research station Y before visiting research station Z is _______. 
    Correct answer is between '0.4,0.6'. Can you explain this answer?
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    A Ph.D. student visits three research stations X, Y and Z in a random ...
    **Understanding the Problem:**

    In this problem, we are given that a Ph.D. student visits three research stations X, Y, and Z in a random order to collect samples. We need to find the probability that the student visits research station Y before visiting research station Z.

    **Possible Orders:**

    Since the student visits the research stations in a random order, there are a total of 3! = 6 possible orders in which the student can visit the stations. These orders are:

    1. XYZ
    2. XZY
    3. YXZ
    4. YZX
    5. ZYX
    6. ZXY

    Out of these possible orders, we are interested in the orders where the student visits research station Y before visiting research station Z.

    **Calculating the Probability:**

    To calculate the probability, we need to determine the number of favorable outcomes (orders where Y is visited before Z) and the total number of possible outcomes (all orders).

    **Number of Favorable Outcomes:**

    From the possible orders listed above, there are two orders where Y is visited before Z: YXZ and YZX. So the number of favorable outcomes is 2.

    **Total Number of Possible Outcomes:**

    As mentioned earlier, there are 6 possible orders in which the student can visit the research stations.

    **Calculating the Probability:**

    The probability of an event is equal to the number of favorable outcomes divided by the total number of possible outcomes. Therefore, the probability that the student visits research station Y before visiting research station Z is:

    Probability = (Number of Favorable Outcomes) / (Total Number of Possible Outcomes)
    = 2 / 6
    = 1 / 3
    ≈ 0.3333

    Since the correct answer is between 0.4 and 0.6, we can round the probability to the nearest tenth:

    Probability ≈ 0.3

    Therefore, the probability that the student visits research station Y before visiting research station Z is approximately 0.3, which is not between 0.4 and 0.6.

    Hence, the given answer is incorrect.
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    A Ph.D. student visits three research stations X, Y and Z in a random order to collect samples. The probability that the student visits research station Y before visiting research station Z is _______.Correct answer is between '0.4,0.6'. Can you explain this answer?
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    A Ph.D. student visits three research stations X, Y and Z in a random order to collect samples. The probability that the student visits research station Y before visiting research station Z is _______.Correct answer is between '0.4,0.6'. Can you explain this answer? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about A Ph.D. student visits three research stations X, Y and Z in a random order to collect samples. The probability that the student visits research station Y before visiting research station Z is _______.Correct answer is between '0.4,0.6'. Can you explain this answer? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A Ph.D. student visits three research stations X, Y and Z in a random order to collect samples. The probability that the student visits research station Y before visiting research station Z is _______.Correct answer is between '0.4,0.6'. Can you explain this answer?.
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