Kayla is competing in a throwing event. A throw is counted as a success if the distance achieved is greater than 30 metres. The probability that Kayla will achieve a success on any throw is $$$0.25$$$. Find the probability that, for a random sample of 10 throws, Kayla achieves at least 3 successes. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_w20_qp_51 Year：2020 Question No：3(b)

Answer:

$1-\mathrm{P}(0,1,2)=1-\left(0.75^{10}+{ }^{10} \mathrm{C}_{1} 0.25^{1} 0.75^{9}+{ }^{10} \mathrm{C}_{2} 0.25^{2} 0.75^{8}\right)$
$1-(0 \cdot 0563135+0 \cdot 1877117+0 \cdot 2815676)$
$0.474$

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,...)

Answer:

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