Among the contestants in a competition are 43 women and 21 men. If 3 winners are randomly selected, what Is the probability that they are all men?

1 Answer
Alan P.
Nov 3, 2015

Probability that all random selectants are men is (approximately) #3.2%#

Explanation:

If there are #43# women and #21# men then there are #64# people in total.

#P("1st is a man") = 21/64#

#P("2nd is a man"|"1st is a man") = 20/63#

#P("1st and 2nd are men") = 21/64xx20/63#

#P("3rd is a man"|"1st and 2nd are men") =19/62#

#P("all 3 are men") = (21/64xx20/63)xx19/62#

#color(white)("XXXXXXXXXX")~= 0.031922#

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