In an examination, there are 10 true-false type questions. Out of 10, a student can guess the answer of 4 questions correctly with probability 3/4 and…

Question

In an examination, there are 10 true-false type questions. Out of 10, a student can guess the answer of 4 questions correctly with probability 3/4 and the remaining 6 questions correctly with probability 1/4. If the probability that the student guesses the answers of exactly 8 questions correctly out of 10 is 27k4^10, then k is equal to

MARKS Content Team · Accepted Answer

Correct answer: 479. Given, A=1,2,3,4:PA=3/4→Correct answer B=5,6,7,8,9,10;PB=1/4 Correct answer Now total ways in which 8 Correct answer is given will be, ⇒Case (i) 4,4:C4434^4·C46·14^4·34^2 ⇒Case (ii) 3,5:C3434^3·14^1·C5614^5·3/4 ⇒Case (iii) 2,6:C2434^214^2·C6614^6 Total probability =14^103^4×15×3^2+4×3^3×6×3+6×3^2 =274^102.7×15+72+2 Now comparing with 27k4^10 We get,K=479

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