Algebra/Trig

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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?

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

  • Algebra/Trig -

    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)! ]

  • Algebra/Trig -

    thanks!

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