A company produces small boxes of sweets that contain 5 jellies and 3 chocolates. Jemeel chooses 3 sweets at random from a box. The company also produces large boxes of sweets. For any large box, the probability that it contains more jellies than chocolates is $$$0.64$$$. 10 large boxes are chosen at random. Find the probability that no more than 7 of these boxes contain more jellies than chocolates. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s20_qp_51 Year：2020 Question No：3(b)

Answer:

$1-\mathrm{P}(8,9,10)=1-\left[{ }^{10} \mathrm{C}_{8} 0.64^{8} 0.36^{2}+{ }^{10} \mathrm{C}_{9} 0.64^{9} 0.36^{1}+0.64^{10}\right]$
$1-(0.164156+0.064852+0.11529)$
$0.759$

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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