document.write( "Question 1200742: The free seats in a movie theater are numbered 1, 2, ..., n. m friends buy tickets one after the other, and seats are assigned to them randomly. What is the probability that they will all get seats with even numbers? Previously, k friends received seats with even numbers. What is the probability that the remaining friends will also get seats with even numbers? ([n, m, k] = [33, 6, 4]) \n" ); document.write( "
Algebra.Com's Answer #848151 by textot(100)\"\" \"About 
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Certainly, let's calculate the probability of all friends getting seats with even numbers given the provided information.\r
\n" ); document.write( "\n" ); document.write( "**1. Determine the number of even-numbered seats:**\r
\n" ); document.write( "\n" ); document.write( "* Total number of seats (n) = 33
\n" ); document.write( "* Number of even-numbered seats = n // 2 = 33 // 2 = 16 \r
\n" ); document.write( "\n" ); document.write( "**2. Calculate the probability for the remaining friends:**\r
\n" ); document.write( "\n" ); document.write( "* Number of friends who already have even seats (k) = 4
\n" ); document.write( "* Number of remaining friends = m - k = 6 - 4 = 2
\n" ); document.write( "* Remaining even-numbered seats = 16 - 4 = 12
\n" ); document.write( "* Remaining total seats = 33 - 4 = 29\r
\n" ); document.write( "\n" ); document.write( "* Probability of the first remaining friend getting an even seat: 12/29
\n" ); document.write( "* Probability of the second remaining friend getting an even seat: 11/28 \r
\n" ); document.write( "\n" ); document.write( "* Probability of both remaining friends getting even seats: (12/29) * (11/28) ≈ 0.162562\r
\n" ); document.write( "\n" ); document.write( "**Therefore, the probability that all friends will get seats with even numbers, given that 4 friends already have even seats, is approximately 0.162562.**
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