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    Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 580

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

DM-Probability -Q20


Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177
+1 vote

An algorithm takes a list of 2^n numbers [ a_1,a_2,...,a_{2^n} ] and replaces it with [ b_1,b_2,...,b_{2^{n-1} } ], where b_1 = max(a_1,a_2),   b_2 = max(a_3,a_4)  and so on. Then it performs the same operation on the resulting list (replacing each pair of consecutive elements with their maximum), and it continues doing the same until there are only two elements left in the list. 

For instance, if the initial list is [3, 7, 6, 8, 2, 1, 4, 5], then after the first run, it becomes [7, 8, 2, 5] and then [8, 5]

Suppose that the elements of the initial list are the integers 1 through 64 in random order. What is the probability that the number 63 will appear in the final two-element list? 

(A). \frac{1}{63}

(B) \frac{1}{4}

(C) \frac{62}{63}

(D) \frac{32}{63}

asked Jul 7, 2020 by gbeditor-2 (72,840 points)
reshown Jul 10, 2020 by gbeditor-2

1 Answer

0 votes
answered Jul 11, 2020 by tsanmol (5,820 points)
we need solutions for this test too, @deepak-gatebook
Answer:

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177
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