document.write( "Question 998452: Of the professors at NSU, 44% are female. If you sign up for 5 classes next semester, find the probability that you will get all female professors. \n" ); document.write( "

Algebra.Com's Answer #616269 by mathmate(429) $\"\"$ $\"About$

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\n" ); document.write( "Problem:
\n" ); document.write( "44% of professors at NSU are female.
\n" ); document.write( "Find probability of having all female professors if 5 classes are chosen randomly.
\n" ); document.write( "
\n" ); document.write( "Solution:
\n" ); document.write( "This problem can be solved using binomial distribution because:
\n" ); document.write( "1. number of steps in experiment is known (n=5)
\n" ); document.write( "2. probability of choosing a class taught by female professor is constant (p=0.44) since each professor could teach multiple courses.
\n" ); document.write( "3. the choice of classes is assumed random (otherwise the probability is 1)
\n" ); document.write( "4. each step (choice of each class) is a Bernoulli experiment, i.e. with two possible outcomes (male or female professor only)\r
\n" ); document.write( "\n" ); document.write( "The probability of choosing all 5 classes taught by female professor(s) is therefore calculated using the binomial distribution with parameters
\n" ); document.write( "n=5 (number of steps)
\n" ); document.write( "p=0.44
\n" ); document.write( "r=5 (5 successes)\r
\n" ); document.write( "\n" ); document.write( "P(5,5,0.44)=C(5,5)*(0.44)^5*(1-0.44)^(5-5)
\n" ); document.write( "=1*(0.44)^5*1
\n" ); document.write( "=0.01649
\n" ); document.write( "
\n" ); document.write( "Answer: the probability of randomly choosing all 5 classes taught by female professors at NSU is 0.01649 \n" ); document.write( "

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