Three fair six-sided dice, each with faces marked 1, 2, 3, 4, 5, 6, are thrown at the same time, repeatedly. For a single throw of the three dice, the score is the sum of the numbers on the top faces. Find the probability that a score of 18 is obtained for the first time on the 5th throw of the three dice. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................
Exam No：9709_s21_qp_53 Year：2021 Question No：4(b)
Answer:
\(\mathrm{P}(18)=\left(\frac{1}{6}\right)^{3}\left[=\frac{1}{216}\right]\)
\(\mathrm{P}(18\) on 5 th throw \()=\left(\frac{215}{216}\right)^{4} \times \frac{1}{216}\)
\(0.00454\)
\(\mathrm{P}(18\) on 5 th throw \()=\left(\frac{215}{216}\right)^{4} \times \frac{1}{216}\)
\(0.00454\)
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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