{"id":20332,"date":"2024-04-15T05:51:28","date_gmt":"2024-04-15T05:51:28","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=20332"},"modified":"2024-04-15T05:51:28","modified_gmt":"2024-04-15T05:51:28","slug":"two-white-and-two-black-balls-kept-in-two-bins-are-arranged-in-four-ways-as-shown-below-in-each-arrangement-a-bin-has-to-be-chosen-randomly-and-only-one-ball-needs-to-be-picked-randomly-from-the-ch","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/two-white-and-two-black-balls-kept-in-two-bins-are-arranged-in-four-ways-as-shown-below-in-each-arrangement-a-bin-has-to-be-chosen-randomly-and-only-one-ball-needs-to-be-picked-randomly-from-the-ch\/","title":{"rendered":"Two white and two black balls, kept in two bins are arranged in four ways as shown below. In each arrangement, a bin has to be chosen randomly and only one ball needs to be picked randomly from the chosen bin. Which one of the following arrangements has the highest probability for getting a white face picked? A. B. C. D."},"content":{"rendered":"

[amp_mcq option1=”nan” option2=”nan” option3=”nan” option4=”nan” correct=”option4″]<\/p>\n

The correct answer is D.<\/p>\n

In arrangement D, there are two white balls in the first bin and one white ball in the second bin. When a bin is chosen randomly, the probability of choosing the first bin is $\\frac{1}{2}$. When the first bin is chosen, the probability of picking a white ball is $\\frac{2}{3}$. Therefore, the overall probability of picking a white ball in arrangement D is $\\frac{1}{2} \\times \\frac{2}{3} = \\frac{2}{3}$.<\/p>\n

In arrangement A, there is one white ball in each bin. When a bin is chosen randomly, the probability of choosing either bin is $\\frac{1}{2}$. When either bin is chosen, the probability of picking a white ball is $\\frac{1}{2}$. Therefore, the overall probability of picking a white ball in arrangement A is $\\frac{1}{2} \\times \\frac{1}{2} = \\frac{1}{4}$.<\/p>\n

In arrangement B, there are two white balls in the second bin and one white ball in the first bin. When a bin is chosen randomly, the probability of choosing the second bin is $\\frac{1}{2}$. When the second bin is chosen, the probability of picking a white ball is $\\frac{2}{3}$. Therefore, the overall probability of picking a white ball in arrangement B is $\\frac{1}{2} \\times \\frac{2}{3} = \\frac{1}{3}$.<\/p>\n

In arrangement C, there is one white ball in each bin. When a bin is chosen randomly, the probability of choosing either bin is $\\frac{1}{2}$. When either bin is chosen, the probability of picking a white ball is $\\frac{1}{2}$. Therefore, the overall probability of picking a white ball in arrangement C is $\\frac{1}{2} \\times \\frac{1}{2} = \\frac{1}{4}$.<\/p>\n","protected":false},"excerpt":{"rendered":"

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