In a certain large college, $$$22 \%$$$ of students own a car. 16 students from the college are chosen at random. Find the probability that the number of these students who own a car is at least 2 and at most 4 . ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s20_qp_53 Year：2020 Question No：2(b)

Answer:

$\mathrm{P}(2,3,4)={ }^{16} \mathrm{C}_{2} 0.22^{2} 0.78^{14}+{ }^{16} C_{3} 0.22^{3} 0.78^{13}+{ }^{16} C_{4} 0.22^{4} 0.78^{12}$
$0.179205+0.235877+0.216221$
$0.631$

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,...)

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