The members of a men’s club have a choice of wearing black or red vests to their club meetings. A study done over a period of many years determined that the percentage of black vests worn is 60%. If there are 10 men at a club meeting on a given night, what is the probability, to the nearest thousandth, that at least 8 of the vests worn will be black?

Question

I know you're supposed to use combinations, but how do you write it all out?

Answer 1

BINOMIAL DISTRIBUTION, yes uses Combinations

n = 10
probability of black = .6
probability not black = .4

prob 8 = C(10,8) .6^8 .4^2
= 45*.6^8*.4^2 = .121

prob 9 = C(10,9) .6^9 .4^1
= 10 *.6^9 * .4 = .040

prob 10 = C(10,10) .6^10 .4^0
= 1 *.6^10 * 1 = .006

sum = .121+.040+.006 = .167

I got the Combinations from Pascal's triangle but you can use a table or calculate
C(n,k) = n!/[ k! (n-k)! ]

Answer 2

thanks!