In a certain region, the probability that any given day in October is wet is $$$0.16$$$, independently of other days. Find the probability that, in a 10-day period in October, fewer than 3 days will be wet. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_w21_qp_52 Year：2021 Question No：5(a)

Answer:

${[\mathrm{P}(0,1,2)=]{ }^{10} \mathrm{C}_{0} 0.16^{0} 0.84^{10}+{ }^{10} \mathrm{C}_{1} 0.16^{1} 0.84^{9}+{ }^{10} \mathrm{C}_{2} 0.16^{2} 0.84^{8} }$
${[=0.17490+0.333145+0.28555] }$
0.794

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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