In Greenton, 70\% of the adults own a car. A random sample of 8 adults from Greenton is chosen. Find the probability that the number of adults in this sample who own a car is less than 6 . ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ A random sample of 120 adults from Greenton is now chosen.
Exam No：9709_m20_qp_52 Year：2020 Question No：5(a)
Answer:
\(1-\mathrm{P}(6,7,8)\)
\(=1-\left({ }^{8} \mathrm{C}_{6} 0.7^{6} 0.3^{2}+{ }^{8} \mathrm{C}_{7} 0.7^{7}
0.3^{1}+0.7^{8}\right)\)
\(=1-0.55177\)
\(=0.448\)
Alternative method for question \(5(a)\)
\(\mathrm{P}(0,1,2,3,4,5)\)
\(=0.3^{8}+{ }^{8} \mathrm{C}_{1} 0.7^{1} 0.3^{7}+{ }^{8} \mathrm{C}_{2} 0.7^{2} 0.3^{6}+{ }^{8} \mathrm{C}_{3} 0.7^{3} 0.3^{5}+\)
\({ }^{8} \mathrm{C}_{4} 0.7^{4} 0.3^{4}+{ }^{8} \mathrm{C}_{5} 0.7^{5} 0.3^{3}\)
\(=0.448\)
\(=1-\left({ }^{8} \mathrm{C}_{6} 0.7^{6} 0.3^{2}+{ }^{8} \mathrm{C}_{7} 0.7^{7}
0.3^{1}+0.7^{8}\right)\)
\(=1-0.55177\)
\(=0.448\)
Alternative method for question \(5(a)\)
\(\mathrm{P}(0,1,2,3,4,5)\)
\(=0.3^{8}+{ }^{8} \mathrm{C}_{1} 0.7^{1} 0.3^{7}+{ }^{8} \mathrm{C}_{2} 0.7^{2} 0.3^{6}+{ }^{8} \mathrm{C}_{3} 0.7^{3} 0.3^{5}+\)
\({ }^{8} \mathrm{C}_{4} 0.7^{4} 0.3^{4}+{ }^{8} \mathrm{C}_{5} 0.7^{5} 0.3^{3}\)
\(=0.448\)
Knowledge points:
5.4.2 use formulae for probabilities for the binomial and geometric distributions, and recognise practical situations where these distributions are suitable models (Including the notations B(n,p) and Geo(p). Geo(p) denotes the distribution in which for r = 1,2,3,...)
Solution:
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