[tex]\begin{gathered} The\text{ binomial probability distribution is given in the following form:} \\ P\text{ = nCx \lparen p}^x)(q^{n-x}) \\ Finding\text{ the probability of at least 6 failures means the probability of 6 or 7 failures.} \\ This\text{ corresponds to 1 or 0 successes.} \\ P(1)\text{ = 7C1 \lparen9\%}^1)(91\%^6) \\ \text{ =0.3278} \\ P(0)\text{ = 0.5168} \\ Probability\text{ of at most one success \lparen at least 6 failures\rparen} \\ =\text{ 0.844 = 84.5\%} \end{gathered}[/tex]
