Question 450068
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Hi,
Note: The probability of x successes in n trials is: 
P = nCx* {{{p^x*q^(n-x)}}} where p and q are the probabilities of success and failure respectively. 
In this case p(failing) = .20 and q(passing) = .80   |the failure rate is 20%.
nCx = {{{n!/(x!(n-x)!)}}}
Of 15 students registered in the freshman class;
 P(all pass) = (.80)^15 = .0352
P(at least 1 fails) = 1 - P(none failing) = 1 - .0352 = .9648
How many freshman are likely to pass? .80*15 = 12

An algebra class has 18 girls and 14 boys. 
Five tickets to a concert have just been made available to the class. 
The students to get the tickets will be chosen at random.
What is the probability that:
a) five girls are chosen = 18C5/32C5 = 8568/201,376 = .0425
  nCx = {{{n!/(x!(n-x)!)}}}  18C5 =  18!/(5!13!) and 32C5 = 32!/5!27!
These can be found with a calculator that has a factorial function.

b) five boys are chosen = 14C5/32C5 = 2002/201,376 = .0099
c) at least 1 girl is chosen? 1 - P(all boys) = 1 - .0099 = .9901
d) How many girls are likely to be chosen? (18/32)*5 = 2.8