Mathematics

Theme:

Probability / प्रायिकता

Q25 2014, Probability

Six identical cards are placed on a table. Each card has number '1' marked on one side and number '2' marked on its other side. All the six cards are placed in such a manner that the number '1' is on the upper side. In one try, exactly four (neither more nor less) cards are turned upside down. In how many least number of tries can the cards be turned upside down such that all the six cards show number "2' on the upper side?

एक मेज़ पर 6 एकसमान कार्ड रखे हुए हैं। प्रत्येक कार्ड के एक फलक पर संख्या '1' व इसके दूसरे फलक पर संख्या '2' अंकित है। सभी छह कार्ड ऐसे रखे हुए हैं कि संख्या '1' वाला फलक ऊपर की तरफ है। एक प्रयास में, तथ्यतः चार (न कम और न ही उससे अधिक) कार्डों को पलटा जाता है। कार्डों को न्यूनतम कितने प्रयासों में ऐसे पलटा जा सकता है कि सभी छह कार्डों के ऊपर संख्या '2' दिखे ?

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1. Correct Answer: Option A: 3
2. Explanation:
     To solve this problem, we need to determine the minimum number of tries required to have all six cards showing the number '2' on the upper side. Initially, all cards show '1'.
     Step-by-step Process:
     ● Try 1: Turn any four cards upside down. Now, four cards show '2' and two cards show '1'.
     ● Try 2: Turn any four cards again. This can be done in such a way that the two cards showing '1' and two cards showing '2' are flipped. After this try, four cards will show '1' and two cards will show '2'.
     ● Try 3: Turn any four cards again. Choose the four cards that are currently showing '1'. After this try, all six cards will show '2'.
     Therefore, the least number of tries required to achieve all cards showing '2' is 3.

Mathematics

Q25 2014, Probability

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Mathematics

Q25 2014, Probability

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