Chapter 10 Counting Methods and Probability - 10.6 Construct and Interpret Binomial Distributions - 10.6 Exercises - Skill Practice - Page 728: 31

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Using the formula for binomial experiments, the probability is: $P(k\geq 10)=P(k=5)+P(k=10)+P(k=11)+P(k=12)+P(k=13)+P(k=14)+P(k=15)\\=_{15}C_{10}(0.75)^{10}(0.25)^{5}+_{15}C_{11}(0.75)^{11}(0.25)^{4}+_{15}C_{12}(0.75)^{12}(0.25)^{3}+_{15}C_{13}(0.75)^{13}(0.25)^{2}+_{15}C_{14}(0.75)^{14}(0.25)^{1}+_{15}C_{15}(0.75)^{15}(0.25)^{0}\\\approx0.85163$