document.write( "Question 1193467: Research finds that of the students entering a degree program, 90% will successfully complete it. In 2018, 15 students commenced the course. Calculate the probability that:
\n" ); document.write( "I) all 15 students will successfully complete the course.
\n" ); document.write( "II) only one student fails.
\n" ); document.write( "III) no more than two students fail.
\n" ); document.write( "I) at least two students fail. \n" ); document.write( "

Algebra.Com's Answer #825493 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "Research finds that of the students entering a degree program, 90% will successfully complete it.
\n" ); document.write( "In 2018, 15 students commenced the course. Calculate the probability that:
\n" ); document.write( "I) all 15 students will successfully complete the course.
\n" ); document.write( "II) only one student fails.
\n" ); document.write( "III) no more than two students fail.
\n" ); document.write( "I) at least two students fail.
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\n" ); document.write( "\n" ); document.write( " All these problems/questions are about binomial probability distribution.\r
\n" ); document.write( "\n" ); document.write( " So, use the related standard formulas.\r
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document.write( "(i)    P =  = 0.2059   (rounded).    ANSWER\r\n" );
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document.write( "(ii)   P =  =  = 0.34315   (rounded).     ANSWER\r\n" );
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document.write( "(iii)  \"No more than two students fail\" means 0, 1, or 2 students fail\r\n" );
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document.write( "       P = P(0 fail) + P(1 fails) + P(2 fail) = \r\n" );
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document.write( "         =  +  +  = \r\n" );
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document.write( "         =  = 0.8159    (rounded).    ANSWER\r\n" );
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document.write( "(iv)  \"at least two students fail\" means that no more than 1 student pass\r\n" );
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document.write( "       P = P(0 pass) + P(1 passes) =  +  =  = 1.36*10^(-13).     ANSWER\r\n" );
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