2 The state legislative council has been charged with sex di

2. The state legislative council has been charged with sex discrimination in hiring. Last year it hired only 3 women out of 12 new employees. The civil service lists show that women comprise 40% of the qualified applicants for these jobs. What is the probability of hiring three or fewer women if the legislative council does not discriminate? 3. A trick coin has been weighted so that the probability of heads is 0.8 and the probability of tails is 0.2. a. If you toss the coin 100 times, how many heads would you expect on the average? b. What is the probability of obtaining at least 92 heads in 100 tosses?

Solution

2) let P(x) be probability of hiring x number of women
then probability of hiring 3 or fewer women = P(0)+P(1)+P(2)+P(3)
now P(0) = (0.6)¹² =0.00217
P(1) = (0.4)(0.6)¹¹ = 0.00145
  P(2) = (0.4)²(0.6)¹⁰ = 0.00096
  P(3) = (0.4)³(0.6)⁹ = 0.00064
therefore P(x<=3) = P(0)+P(1)+P(2)+P(3) = 0.00524

2) let H-be getting a head and T-be getting a tail
  given P(H)=0.8
a) on average in 100 tosses we will get p(H) = 0.8x100 = 80
b) probability of getting 8 tails or less = P(T=0)+P(T=1)....+P(T=8)
     = (0.8)¹⁰⁰+(0.8)⁹⁹(0.2)+(0.8)⁹⁸(0.2)²+(0.8)⁹⁷(0.2)³.....+(0.8)⁹²(0.2)⁸
= (0.8)⁹²[(0.8)⁸+(0.8)⁷(0.2)....+(0.8)(0.2)⁷+(0.2)⁸]
       = 2.716037x10^-10