Question

#800. Gender and Handedness Below is survey results about student handedness and their gender. If we select 3 students randomly without replacement, what is the probability that not all are female? Left Handed Ambidextrous Right Handed Totals Male 23 26 250 299 Female 23 381 430 Totals 46 631 729 You can answer in fraction, decimal, or percentage. If your answer is in decimal, make sure to include at least 2 NON-ZERO digits after the decimal point (for example, 0.00015). If your answer is a percentage, you have to include the % sign in your answer. symbolic expression

Answer 1

Number of ways to select r items from n, nCr = n!/(r! x (n-r)!)

P(not all three are female) = 1 - P(all three are female)

= 1 - Number of ways to select 3 females from 430 / Number of ways to select any 3 from 729

= 1 - 430C3/729C3

= 1 - 0.20

= 0.80